Here's the NGram for *cashpoint* versus *cash machine* from the British English corpus:

![][1]


  [1]: https://books.google.com/ngrams/chart?content=cashpoint%2Ccash%20machine&year_start=1800&year_end=2000&corpus=18&smoothing=3&share=&direct_url=t1%3B%2Ccashpoint%3B%2Cc0%3B.t1%3B%2Ccash%20machine%3B%2Cc0

As one can see *cashpoint* is 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 hard evidence!

Nonetheless, as pointed out in several posts, *dispenser* and *hole in the wall* are also frequently used.