If you can easily make double and you'd be happy with double, ask for double. (BTW it's crucial to specify location and currency when discussing compensation online. 22K pounds in a non-London location is very different than $22K USD in a major US city, for example)

Best case, you get what you ask for.

Worst case, they say no and you're right back where you started.

Your negotiating position will be 10X more effective if you're actually willing to walk away from this company. If they think you're going to stay regardless of how much they pay you, they might try to call your bluff and continue underpaying you.