Fun "activity" date ideas(central london)

Hey I need fun activity date ideas I can do in central london with a girl(shes 18, I'm 23) Something fun like bowling, pool, games in an arcade, riding a tug boat, galleries and fun places like madam tussauds but without the huge price tag lol.... Just give me loads of suggestions please and tell me where it is co I can figure out if its accessible or not Thanks!

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