Should I upgrade to DSLR camera? If so which one?

I have been doing photography for a couple of years and would consider myself somewhat knowledgeable on the subject. I take photos of lots of different things, anything that looks interesting really.

I have mainly been using a small digital compact and my iPhone to take photographs of things because these are the only good cameras I own. The problem comes with flexibility and processing. I don't have enough options to do really interesting shots because most of the setting are automatically adjusted by the camera. I also can't put different lenses on my camera to get different kinds of photos. Also, whenever I try to make my 'photos look better on a pc by editing them, all these weird artefacts of the image show up and it ends up looking blurry and grainy.

Do I need a DSLR to go further with my hobby? If so, which one? (Have a budget of around £250-350)

If you enjoy photography and want to continue it as a hobby, sure go ahead and buy a DSLR. As technology moves on, they are becoming more and more affordable. If you want to start out with something cheap, but still very capable, you should look at models like the Canon T3, T2i, T3i, Nikon D3000, D3100, D5000, Pentax K-30. Most of these are older models and have been/are being replaced, that means you can find them cheaper or even refurbished models that should be cheaper still.

Most DSLRs come with a standard stock 18-55 lens, which should be fine for a beginner until you find out what kind of things you like to shoot and if you need another lens. If you decide to go the portrait/low light/narrow depth of field way, a 50mm f/1.8 lens is good and if you go the bird/far away in the distance way, a 50-200 or 70-300 lens is something you should consider.

If you are serious about wanting to learn the more technical side of photography then yes, a DSLR would be suitable.

All the major manufacturers make similar models at similar price points. With your budget you could just about scrape an entry level DSLR Go into a camera shop & try out models from Canon, Nikon or whoever takes your fancy. Buy the one that feels best for you.

For example the Nikon D3200 is £320 at Currys.

If you do buy a DSLR though, don't just use it on Auto! Take the time to learn about exposure (ISO, aperture & shutter speed), lighting & composition. Join a local photography club if you can.

And the reason your images look poor when post processing is that the small sensor in the compact or your phone leads to small, low resolution images and they are jpgs. Post processing really needs use to start out with full data off a reasonably sized sensor (like a DSLR) - and that means shooting in raw.

For your budget you are at the low end of the spectrum, and also limited to the number of lenses you can have initially.
A basic camera should have the Kit lens of 18-55mm
This is fine to get started with and allows you to experiment.
Look at online auctions for those photographers that are upgrading. They may be some decent second hand buys out there.
Decide on the manufacturer, as in the future if you change brand, their lenses will not work on a new one
The most common are canon, nikon and sony.
on ebay a used package - http://www.ebay.co.uk/...0937044477

a quick search found a new camera around your budget http://www.hdewcameras.co.uk/canon-eos-600d-body-with-18-55-is-ii-lens-kit-835-p.asp

New is obviously better as you get the warranty.