Any large project involving your home should be undertaken by as reputable a company as you can find and afford. Asking friends and neighbours for recommendations should be your first action.
Not only could poor work devalue your home but using a cheap guy around the corner could prove your undoing if he decides not to respond to your calls if there are problems.
Also you will probably have to get a builder to build the brick base so get some recommendations .. any extensions going on in your area? Look at their brickwork and if it is neat, get a price from them, in fact get three prices and go for the middle one. Don't pay them anything up front either.
Thank you all so much for the advice. We have a guy coming round to give us an estimate tomorrow. He's from the same firm who did our double glazing 8 years ago, and they did a great job with great after care so fingers crossed that we can afford it! Once again, many thanks.