2021 Update: I am now FULLY BOOKED from March to December with all my regular customers.
So if you are a new customer I have a son that shears, but he does not drive yet, so, if you don't mind picking him up (from Horncastle, Lincolnshire (LN9)) he might be able to fit you in. Nathan's number is on the 'Other Sheep Shearers' link above (he does not live with me).
Another thing you could try is call some of the shearers I know who are listed on the 'Other Sheep Shearers' page, just follow the link above.
You could also try hunting down your lacal shearer, not an easy task I dare say. Start by looking round for other sheep, then try and track down who owns them, ask them who shears them and then ask that shearer if they will come to do yours. If you only have a few pet sheep then the shearer might at first say no, and that is often because they do not want to charge enough to make it worth their while. Shearers normally change about £2.50/sheep, so that will not be worth them turning up, so if you offer them £50 then they may very well say yes!