Farringdon (Metropolitan, Circle, Hammersmith and City) - we are just accross the road.

Farringdon train station in on the other side of the road.

The 55, 63, 243, N35, N55, N63 go through Farringdon. Or the 4, 8, 17, 25, 38, 214 and 242 stop locally, about 5 mins walk to the Castle.