I also walked past this place the other day too. Apparently Iron Maiden played their first gigs at the Cart and Horses, that's before they experimented with a keyboard player and then deciding to drop that sound. according to sing365.com the first gig was in 1977 and to put that in context, I would have been 3 and the film Star Wars would have just been released in the UK too. Going by the sign they're still keeping it rock ad with a 2am license.
I'll be popping in for a snake bite at a later date.