College student staying in London for 3 weeks and would like to visit as many sites as possible. Is there a museum/attraction pass for students that is longer than the 1, 3 & 6 day pass?
Most all of the major museums in London are free:
http://www.timeout.com/london/museums/free-museums-in-london
For the reason Michael stated, I've never found a reason to recommend a museum pass in London.
Just as charities are starved for money here in the US, I did notice that almost every touring, temporary, or special exhibition in "free" London museums has a substantial charge. Tate Modern, for example, had two separate special shows (both of them packed with a waiting line too, Matisse Cut-Outs and the just-closed Richard Hamilton), each around 14 Pounds. And regular admissions at most places with a charge are "marked up" by a "discretionary" 1 Pound matched-donation price. You have to ask to have it taken off, but of course no one does.
I don't mean to sound whiny, I'm just reporting on the OP topic. US charities are doing everything they can to augment income. For example, annoying $2 "Facility Charges" at performing arts centers everywhere ...
Putting on a 'voluntary' donation on top of posted admission prices means the institution can claim back income tax on the lot via gift aid, but this only works for UK tax payers. You may also notice in the small print that this possibly allows admission for 12 months rather than just a day.
A lot of museums don't have a compulsory charge at all, but they don't run on fresh air, hence the donation bins.
Some have gone back to charging because they couldn't cope with the visitor surge when they became free (eg parts of the Greenwich Observatory).