Easter isn't really a big deal in the UK. I'd expect places to be closed over Christmas but probably not Easter.
There may be reduced opening hours and smaller venues and shops may be closed but London is a vibrant city so I expect you'll find plenty to do.
If there are specific places you want to visit it might be worth checking their website or emailing them to confirm. Or just try booking tickets for those dates and you'll see.
If anything because people have time off you might find there's more going on at Easter than other times. You'll certainly find egg hunts and other such activities for kids at tourist attractions