I'm looking for a film which I think was made in Black & White. I believe it was a comedy. Someone worked at Mi5 or some such office and their job was an assassin unfortunately they couldn't go through with it but a homeless person helped them out by committing the assassination for them and they were then paid. One of the assassination was by pushing someone under a train or a tube train.

It's been suggested by my sources that your movie may be 1965's The Liquidator, a British comedy about a spy who sub-contracts his killings. It has a scene where he can't bring himself to push a woman in front of a train, so he later hires a bloke to do so.