what to do on a Sunday afternoon in London

Am stuck. Have to organise a 'hen' type event for Sunday 4th June in Central London. A picnic is the obvious choice, but far too weather dependent. Looking for fun and whacky ideas of what to do with 8 women, that does not cost a small fortune, and will not leave us with sprained or broken limbs (rollerblading is a no no!) Would appreciate all the help I can get. Alcohol can be involved, but preferably not a whole afternoon/evening in a pub - unless there is a theme....would love to karaoke.

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