Does anyone have any good recommendations, looking in the £300 to
£400 price range?
In that price range I think your best bet will be a ex-corporate machine. There are lots of sellers of these on ebay. But you do need to be careful with the spec of what you go for. Alternatively there are the computer fairs that roam the country, that will allow you to get hands on, take a live USB stick to check the exact config and the free drivers are available for all the hardware.
For a bit more I was really impressed with entroware, saw them at oggcamp, nice machines, and fully support open source. We should encourage these sorts of suppliers rather than buying from vendors that don't offer open source alternatives.