So why was Tony Blair not invited to the Royal Wedding?

Three interesting possibilities:
1) From this 2007 Mail article :

'For a modern monarch to rebuke a serving Prime Minister is extremely rare.

The Queen has done it only once in her reign - and the object of her disfavour was Tony Blair. The telling-off came in the early days of the Blair premiership.

The occasion was the State Opening of Parliament which followed a few days after the 1997 election.

In a massive challenge to the authority of the British monarchy, Tony and Cherie Blair sought to capture the event for themselves.

They made the unprecedented decision to walk from Downing Street to Parliament while the Queen arrived in her royal coach.

This decision mattered deeply because the drama of the state opening is all about the Queen: her departure by stagecoach from Buckingham Palace, her arrival in Parliament through the Sovereign's Entrance under the Royal Tower, the putting on of the crown and robes of state before the final entrance to the House of Lords' chamber.

...

An air of understated but definite menace at all times lay behind New Labour's dealing with the monarchy.

In 1997 the New Labour manifesto gave an assurance that "we have no plans to replace the monarchy".

This undertaking - as the more intelligent courtiers grasped - would not have been made had an attack on the British monarchy not been on the agenda.

Plans to get rid of the Royal Yacht were at the heart of the election campaign, sending out what pollsters called a "dog whistle" message - not heard by everyone - that the party was opposed to the Royal Family.

In private briefings with allies in the Press, New Labour in government was openly hostile, with senior figures inside Downing Street freely attacking the Royal Family.

In private the Blairs and their official entourage showed a startling lack of respect.

For the first time since the Queen acceded to the throne in 1952, relations between senior members of the Royal Family and the Prime Minister became actively unpleasant.

This reflected a new attitude from the Prime Minister and those around him. His aides were capable of great impatience with royal procedures, often going beyond rudeness.

The worst offenders were Tony Blair's wife, Cherie, and his adviser Alastair Campbell. She would refuse to curtsy when she met the Queen, and was capable of blanking out senior members of the Royal Family when she encountered them.

She made no pretence at all that she enjoyed royal occasions, and often, through physical and other signals, made it clear that she would rather be elsewhere.

This private lack of respect towards the Royal Family came to be reciprocated. Once Cherie Blair told Princess Anne to "call me Cherie". "Mrs Blair will do," replied the Princess Royal.

...

Shortly after he was appointed Foreign Secretary in 2002, Jack Straw gave an interview to the Guardian in which he referred twice to Tony Blair as "head of state".

At one stage the Downing Street website described how the Queen enjoyed audiences with Tony Blair, and not the other way around.

The Treasury moved fast to remove the royal coat of arms from its logo and drop the initials HM from its official title. The change was said to "reflect a modern image under Gordon Brown's stewardship".

During a visit to Kosovo Tony Blair referred to "my" armed forces, oblivious to the important constitutional fact that British troops owe their allegiance to the monarch as head of state.

Meanwhile the Government set out to write the monarchy out of British public life, an audacious task involving the unravelling of 1,000 years of history.

The most important example of this was the very serious attempt by the Labour government to create a new national identity.

This involved disregarding the institutions of the state that had historically been at the heart of Britain, and replacing them by others, such as a new national day.

In a series of public statements Labour ministers argued that Britain should be defined by abstract values such as fairness. They never mentioned the monarchy.

A series of speeches by Gordon Brown about "Britishness" - an ugly and artificial word - systematically excluded the British monarchy, even though the Queen is head of state and the monarchy encapsulated Britain's long history better than any other institution, including Parliament.

...

Attempts to intrude on the territory of the monarch were to become a repeated feature of the Blair period in office.

The death of Diana, Princess of Wales in August 1997 gave a massive opportunity for the Prime Minister.

The words he uttered on the morning after the tragedy, in which he expressed his devastation at the death of Princess Diana, were brilliantly chosen and widely praised for expressing the mood of the nation.

Members of the Royal Family had been trained from birth to suppress their emotions, exercise restraint and show dignity.

The political philosopher David Marquand noted that when Diana died "the royals behaved as they had been taught to do: as symbols of the state, quintessential inhabitants of the public domain, with all its emotional austerity and self-control".

Previous generations of politicians, had shown comparable restraint (and the Tory leader William Hague was criticised for an inadequate expression of grief when he made his statement about the Princess's death).

Tony Blair, in his response, was at his most formidable as a politician. By showing open grief, and by using the phrase "people's princess", he was opening up new ground and massively extending the territory of the Political Class.

Five years later, following the death of the Queen Mother, the Prime Minister sought to intrude once again into the public domain occupied by the British Royal Family.

Within 24 hours of the Queen Mother's death on March 30, 2002, Tony Blair was seeking to enlarge his public role in the funeral.

Downing Street officials persistently rang Lt-General Sir Michael Willcocks, known as "Black Rod", putting pressure on him for the Prime Minister to play a more prominent part than had originally been planned, including the astonishing proposal that Tony Blair should break with precedent and walk from Downing Street to Westminister Hall in order to meet the Queen Mother's coffin. This pressure was rejected.

Sir Michael also faced intimidation in the wake of the funeral. He refused to endorse the false Downing Street claim that Tony Blair had not tried to muscle in.

After he withstood constant pressure, Tony Blair's press secretary Alastair Campbell vowed that "we'll get him one day".

The problem for Tony Blair and New Labour is simple to explain. The ten-day remembrance period for the Queen Mother left him without a central role.

At state events such as the Queen Mother's funeral, the Prime Minister of the day ranked lower than politically far less significant figures such as the Lord Chancellor and the Speaker of the House of Commons.

This was not, of course, a threat to the Government: the funeral of the Queen Mother had nothing at all to do with politics as it had conventionally been practised.

But it was a challenge specifically to New Labour, because the commemoration period for the Queen Mother claimed back a part of British public life, normally outside politics, that New Labour has asserted as its own.

This meant that the queues for the lying-in-state were almost as disconcerting for New Labour as the grief for Princess Diana had been for the Royal Family five years previously.

The great celebration of the Queen Mother's life was an affront to the Political Class because it was a reminder of the existence of a Britain whose loyalties and allegiances went far deeper than party, but had everything to do with the love of Queen, country, village, school, town and family.

These allegiances were wholly compatible with voting Labour, Liberal Democrat, Tory or any number of other political parties.

They are not, however, compatible with totalitarian politics, which lays claim to space that lies well outside party politics as it has always been practised in Britain.

There is little doubt that New Labour in power yearned to make a full-frontal and lethal attack on the British monarchy. There is little doubt that only the sustained popularity of the Queen prevented it from doing so.

Extracted from THE TRIUMPH OF THE POLITICAL CLASS by Peter Oborne'

2. Alex Masterley thinks there might be another explanation:

'Rules for wedding invites, particularly Royal ones

...

Which leads us to the issue of the preferment of Arab dictator princelings to Scottish ex-prime ministers. Now let's face it, if it came down to a personality test, it would probably be a dead heat, but that isn't what counts. Forget protocol (there is none), and consider the feelings of the young couple.

Which would they rather have at their wedding? The one who isn't just going to give them a full dinner service, but also a pair of his and hers matching Lamborghinis and a year's supply of petrol. With some wedding guests, excessive lavishness is de rigueuer.

... but not Phoney Bliar and Prudence McDoom.'

3. Or was it Prince William's decision:

'A prominent historian has claimed that former British Prime Minister Tony Blair was not invited to Friday’s royal wedding because Prince William dislikes the politician and not of political things.

“I think the plain truth is that for all sorts of reasons, (Prince) William developed a powerful dislike of Mr Blair,” David Starkey told Sky News during a debate on the monarchy.

“Particularly the way in which he intervened at his mother’s funeral service. These are not political at all, they are personal choices,” he said.'

Whatever the reason I must say that it was pleasant not to have see the unbearably smug Tony Blair and his ever grasping wife, Cherie, sitting in the Quire/Choir. I presume that the Metropolitan Police were also relieved at not having to accommodate his personal protection team as well as not having to keep an eye on Cherie in case she decided to acquire some souvenirs to sell on eBay...