Hundreds of tours take place in London every day without contravening the 'mass gathering' laws (can you see where this is going).
I was thinking - would it be possible to organise a 'Charity Tour' of some of the sites (Houses of Parliament, Buckingham Palace, etc) for a largish group of people. Have a token cost for everyone which will give you a free commemerative t-shirt (something simple like an anti-war slogan or the declaration of human rights dealing with free speech or anti-torture with the tours dates and maybe a witty non-threatening/political commentquote on the back). The fee is optional and any up to the each person how much they pay (with a reccommend amount covering base t-shirt price but waved for those who couldn't afford that). Any additional cash raised would be donated to a good cause - for instance Amnesty International.
This way we could have a bundle of people going round a few sites of note taking photos and having fun, raising money for charity :p
If we didn't get shouty at the police then they shouldn't really have any grounds to stop us, although I think in some areas we'd probably still get a talking to...