HolyMonthOf
IMO and I am not a lawyer so it's just my opinion.
What you could do as a starter is write a strongly worded letter to the management of the Science Museum. Reporting what you have just told us. You told the man that he was in the Ladies and he acknowledged it. When you mentioned it to Security, they appeared not to take any action, because you later saw the man wandering around the Museum. Meanwhile your enjoyment of the evening was spoilt. You could then ask them when they intend to accept their responsibility under the law - that Toilets should only be used by the Sex designated at the door. I suspect you will get some mealy mouthed response or they will do a Sunderland Minster and badge the Ladies as mixed sex.
I suspect the problem will be that there doesn't appear to be any law to stop someone going into the loos of the wrong sex.
So what should we do if this sort of thing happens to us - as long as we are not desperate to go to the loo, immediately leave and find security to advise them that they need to tell the man to leave?
Would we be in order to take a photo of the man leaving the loos? Such a photo would make it clear to the management that they are not enforcing single sex provisions and could be taken to court, and that the law is clear that when single sex facilities are provided, that it what they should be.
Long post sorry. But given that there is normally a queue for the Ladies in public buildings and never seems to be for the Gents, any man going into the Ladies is most likely seeking validation.