We do, but it is not widespread. My 21 year old son goes to one in London every year, for comic fans. I think it is the main one in the UK.
Years ago I took my daughter to one in Brighton, for ardent fans of the "Buffy the Vampire Slayer" television programme and it's stablemate "Angel". I provided transport, refreshments and otherwise treated it as a photo opportunity.
I was shooting film that day. Strangely none of the shots of the cast came out...