If it is a hardtail MTB and the front forks can be locked then with road tyres difference may be less than you think in terms of speed.
I would stick with what you have got for a while. Get used to riding, make sure you like it and then get a £500 bike. There are just too many compromises on the £300 bikes. Cheap frame, cheap components, cheap wheels. At £500-£600-£750 you will get a lot better bike. I only mention £750 because keeping what you have got for a while will let you save up, and as Gastank says there are some good deals to be had.
There is a Felt 85 that is £800 down to £600, and if you can get another 10% off then £560.
So stick with what you have got, save up a little and then test ride a few.