A massive cedar could run into four figures, but it depends mainly on the amount of work involved. Any decent contractor will give you a fixed price quote, make sure you get it in writing and that it specifies exactly what they will do. There can be a huge difference between the cost of a) just getting it on the ground b) cutting it into manageable pieces so you can shift it and c) both the above and carting it all away.
Its worth getting two or three quotes, be wary of any that seem way cheaper than the others. Poole BC should be able to recommend someone, otherwise there is a list of approved contractors on the Arboricultural Association web site at http://www.trees.org.uk