The patent application itself is quite cheap, around £30 I think. But before you do that you need to do some searches to see if your invention is actually new and therefore patent-able. You can do this yourself (searches are more expensive at around £100-150 each), but you have to know what you're looking for, and you have to be able to understand the descriptive language used, which is rather unique to say the least. Even with my engineering background, I would not be able to write my own patent application with any hope of getting it right, and it has to be absolutely correct if it is to be watertight.
If you're really serious, then you hire a patent agent, who will cost you several thousand, but save you many times that in the long run. If you want to apply for worldwide patents rather than just a UK patent, then multiply that by 10 at least. And you'll still have trouble stopping the Chinese copying your invention.
I only have have one half of a patent to my name (I was a "co-inventor"), and the patent application and agents' work was paid for by the company I worked for. That was back in the days when such an arrangement meant that the company took the royalties, rather than the inventor. It took around 9 months to get to the Pat Pending stage, and another 6 months to get the patent granted in full.
James Dyson is an expert on patents - his autobiography outlines some of the difficulties he has had with his vacuum cleaners over the years, with some very big names openly flouting his patents. Well worth reading.
link:
http://www.ipo.gov.uk/ - look for the 'Patents' link