I'm a programmer currently working in central London (relocated from Italy about 1month ago). While i don't want to publicly disclose my salary, i can tell you that you can expect to do a bit more than double of what you just mentioned. For a junior-mid position you can expect to get something between 45-55k GBP. For a senior position you are supposed to get something between 55k to 70k. This is assuming you are working with a permanent position, if you work as an external consultant you will probably make 400-600GBP/day.

It also hugely depends on the field where you'll be working, financial institutions are well known to offer better wages (but it's mostly a very stressing environment).