Web design can range widely in price, and would need a developer with good experience to give you a relevant quote. Prices can range from £500 into the £100,000's.
I'd say yours would be priced betweek 1-5k but again you'd be better to get a true quote from several companies. Look at small agencies based out of London as prices can also differ (for design we charge almost 75% less than London based design agencies and offer the same thing). Also make sure if you have the idea you get the company to sign a confidentiality agreement, as they could just take your idea and run with it!
Gaz