Does it need to be new?
Also depends on how portable you need it to be?
Personally, I think if you want to be productive in any way at all, then rule out tablets at the moment. They just don’t cut it I don’t think. You need a keyboard, and if you take that, you may as well take a laptop. A l number of the Windows surface reviews comment on how they aren’t really useable with keyboards on the lap, so that may be another factor against the surface.
If I was wanting something new, but to be cheap and small, I’d be looking for a little bit more than £250, and I’d put the money against a small ThinkPad X131e or e130/e135. Something small, but sturdy and would handle the tasks you describe.