Hello Demonmagus --
It's difficult to make suggestions without more context. Are you GCSE or A level? What year? What training or classes is this for, e.g., biology?
Most institutions like the Natural History Museum do take on volunteers during the summer months, usually to do "grunt work" of one sort or another, such as helping to move specimens about. But because such things look good on a CV, they're usually over-subscribed, so if you want to do something like that, you have to apply early.
If this is simply a small project to do in a particular class, and you only have a few days to spend, then it makes sense to pick something you already semi-know the answer to. That way, your trip to London will be fact-gathering and taking photos or samples, and you can then put together a nice report very quickly. To get good marks you either want to show how you got to the answer (i.e., logical thinking) or why something doesn't intrinsically work (i.e., you refute an hypothesis). Vague problems because you didn't have time or the tools won't look good (merely shows you're stupid or lazy!).
One place I'd mention is the Hornimann Museum in south London. Besides having a top-notch public aquarium they were (and presumably still are) involved in captive breeding of cichlids likely to be extinct in the wild (Lake Victoria). So one idea would be to look at how public and home aquaria can be used for conservation, and what the problems are (e.g., too-small gene pool, hybridising by irresponsible aquarists, etc.).
Please note that I was a high school science teacher for a while, and have a fair idea of what is expected for GCSE and A level. In other words, quoting people from Fish Forums as your "references" isn't good enough -- before you start your project you will need to hit the library or a SCIENTIFIC web site (as opposed to Wikipedia).
Cheers, Neale