Removing the chimneys is a fairly straightforward big-hammer job but the difficult bit can be to ensure that the floors are adequately supported after they've been removed. Many houses just keep the chimneys in place.
If you visit a site like screwfix.com or diy.com you can get an idea of raw materials. A basic boiler costs £500 - £600 but, if the system is for you, it's worth spending a little more. Radiators cost anything from £20 to £200 each. It might be worth putting a nice towel radiator in the bathroom. Pipes and valves could be another £100. If fitting is fairly standard involving no more than making a few holes in the walls and pulling up some floor boards, it should be done in half a week's worth of labour.
British Gas will probably be the most expensive option. If you go to www.trustcorgi.com to find some a decent plumbers for more quotes, you should be able to get the figure down to perhaps half the BG figure. If you pay more, you want to be getting something better than a basic system - "designer" radiators, a hi specification boiler and so on. A good plumber should be happy for you to choose the boiler and radiators yourself.