The quick answer is 'as much as you can afford', as you should always buy the best you can when making an important equipment purchase like this. However, the amount of money you are likely to spend on your chainsaw, really depends on what you are looking for and the kind of work you are planning.
There is no point in spending several hundreds of pounds on a large petrol machine if all you what to do is make a handful of kindling every few days but, contrary-wise, don't just plonk a couple of pounds down on something cheap and cheerful that will conk out after a week or so.
MowDirect stocks a variety of quality machines at reasonable prices and you can easily compare features and value by checking out our reviews.
As a very, very rough guide, you should expect to pay from around £60 to £90 for a decent quality, small and simple electric machine up to £250 - £350 for a range topping electric and from around the £110 mark for a basic petrol machine up to over a £1200 for a top flight, heavy-duty petrol model.