It seems strange that "runners" isn't accepted as a correct answer here, when that would be the English term generally used in both the UK and Ireland, with "trainers" very much an American usage.
Are you meaning trainers as in the running shoes footwear?
I have never heard them called 'runners' and I am a native English speaker from the UK. I have heard them called pumps, daps, and more frequently the americanism 'trainers', but never runners. Which part of the UK did you hear this term?
It's interesting that "trainers" is considered an American term- I live in upstate NY and I don't think I've ever heard anyone call this type of footwear "trainers". I agree with JeffA2 in that I would have expected that to be a British thing. Generally everyone (in this part of the country anyway) calls them sneakers. :)