I have been to the London aquarium about 6 times over the past few years, as I am often in London for Business and stay in a hotel close by in Westminster. Unfortunately if you have been to any of the major public aquariums in North America ie. Georgia, Monterey, New England, Shedd etc. you will most likely be quite disappointed with the exhibit caliber of the London Aquarium. The facility is for-profit unlike many of its North American counterparts and was built on shoe string budget although some money was put into renovation on its shark tank earlier this year.
If I was to recommend a public aquarium in the UK I would say that visiting the National Marine Aquarium in Plymouth would be a much better bet if you want to see a world class facility.