I'm thinking about buying a camera?

You'll need something with a large sensor, and full manual control. You'll be running the camera on the bulb setting so a cable release is the minimum requirement, an intervalomter would be a bonus, but they can be costly.

£300 is really quite a small amount of money to be spending on such a thing, and people can eaily spend many thousands on this hobby. In your budget you may find a second hand DSLR may prove to be a better choice as you can get something with the functions you need. Since DSLRs don't normally drop far below the £120 mark for a very old second hand body, you're really looking at a small window here, and we haven't even discussed lenses yet. I think you will be reasonably well off with a Canon T3 or Nikon D3100, but there are more capable cameras out there.

As to lenses, well if you're looking to do star trails, then a wider lens will be more useful, however if you want to capture the actual constellations then you need a telescope or at least an supertelephoto lens, and a barn door tracker or equitorial mount, and this starts to get really expensive.

300 quid might get you a refurbished Nikon D3000. But it won't be good for taking photos of the stars.