I'm very sorry, fatfingers, but I beg to differ on your theory of the orchard.
Attached is a map of the Blake Lane area of Bordesley Green of 1890. One can see that the Custard House - which is halfway down, or up, Blake Lane on the eastern side - was then called the Custard House Tavern.
If you now look at the corner of Green Lane, Blake Lane, Hobmoor Road and Yardley Green Road, on the corner between the last two named roads, you will see a building which was called Custard House. I very much imaging that the tavern - and consequently the pub - took its name from the original Custard House.
Has anyone got any information on the 1890 building?
Might it be just possible that the name is a corruption due to local pronunciation of Customs House? Only a theory. I can't for the life of me imagine why a customs house would be out in the wilds of what was then Warwickshire. db84124