Well, for any trip there are certain costs: transportation, hotel, food, and entertainment.
The closest major airport to Forks, Washington is Seattle. You can fly round-trip between London and Seattle for about $1,000.
There are very few hotels in and around Forks, but for the few there are, figure about $120 a night.
You'll need a rental car to get to Forks and to move around while there. Figure about $100 a day.
If you eat cheap, figure about $50 a day for food.
Entertainment is limited, so let's just say $20 a day for a souvenir or such.
So, you're figuring about $3,000 USD, which is about 1,850 British pounds.
And remember, that reality rarely resembles what you see on television.