Adam Douglas
I think Barclays is trying to do this in my home city of Leeds (which would imply that it is occurring in London and Manchester too, since nothing comes to Leeds /first/). Every Barclays ATM I visit has free Barclays wi-fi. But I find no use for wi-fi as I rather just use 3G/4G mobile internet and tether my laptop when necessary. It's actually faster to set up tethering than the authentication/login process most public wi-fi requires, and 3G/4G is snappy enough considering I just consume and send text (rather than images, video, etc).