Could it be The Liquidator (1965)?
E.
Right, then! Perhaps one of you actual British-types might be able to figger this one out. I have plucked this query from another site and haven't been able to ID the movie myself.
"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."
Some stills of the tube train incident in The Liquidator here:
The Liquidator [1965 feature film]
E.
I haven't received confirmation from the original poster, but Euryale's answer surely seems right to me, so I'm unilaterally declaring it to be the victor.