Here's the NGram for cashpoint versus cash machine from the British English corpus:
As one can see cashpoint appears to be equally as frequent as cash machine in British English, as has been pointed out by many commenters and posters here. This has now been backed up by circumstantial (i.e. NGram) evidence.
Nonetheless, as pointed out in several posts, dispenser and hole in the wall are also frequently used. Anecdotally, I very rarely hear ATM here in London, or in Edinburgh or Devon.
Unfortunately, an NGram for ATM in British English basically throws up thousands of results from books on:
- Asynchronous Transfer Mode