Welcome swifty99
When you say road-bike I'mm assuming that you mean a racing bike, drop bars etc as opposed to a hybrid (straight bars).
Unfortunately £350 buys almost nothing new. Second hand is an option but you need to know a bit.
However, all is not lost.
Decathlon bikes are amazing value. My pal rides one and it's fantastic. However it looks like they are running out at the previous bargain price of £299 with Campag 10 speed. Grab one if yopu can.
http://www.decathlon.co.uk/EN/sport-2-42393914/
But, the Sport 1 looks OK too, not quite as well appointed, but still a bargain price IMO.
http://www.decathlon.co.uk/EN/sport-1-54-57-69567468/
It seems the new Sport 2 comes with Shimano Sora, more carbon and a big price hike.
However, you may want mudguards and some load carrying capacity and this is maybe not the bike for that. Maybe a tourer type? Recently there was a thread about the Claud Butler Dalesman as a budget tourer or take a look at Edinburgh Bicycle Co-operative's own brand range.
Give us more info, type of terrain, previous experience, what you need the bike to do!