Although paranoidfish says that the Hammersmith & City line is not actually connected to the station at Paddington, this is not correct. It's just at the opposite end of the platform to the Bakerloo & Circle lines. Instead of going towards the entrance of the station, go up the platform instead, up the stairs, and across the little bridge. You'll find yourself on the platform for the Hammersmith & City line, both Westbound & Eastbound trains.