Not the whole thing, it's a very labour-intensive job so researchers are unlikely to do it for nothing. You may be lucky enough to have a very keen relative or an aristocratic family, in which case your family tree may be on the net already, but this isn't common. However, there are plenty of free resources to help in your search, and some very kind people who will search small bits (eg census look-ups) free as long as you're nice to them. Look for them at
http://www.ukgenealogy.co.uk/index.html
In addition,
http://www.rootsweb.com
is an immense site full of info on how to get started, searchable databases etc etc, and also has mailing lists by surname and county so you can ask the most likely people for information. Make sure you start off on the right footing though, ask around and get as many names, places, dates etc as you can from your family, look through births/deaths/marriages free in your library, look up parish records if the relevant church is local - it's a very long, slow, frustrating job but extremely rewarding once you start getting somewhere. Beware of red herrings and jumping to wrong conclusions - it really is worth putting in the extra bit of effort to make sure that your information is accurate.