Have you considered any of the online fax providers? These services provide you with a UK telephone number which delivers faxes to you via email attachment. You can also register to send faxes online. Monthly cost ranges from £8 - £15 plus cost per page which again varies. Depends which service you go with.
Not sure if I can post a direct link to the providers but a search on Google for jFax, eFax or YAC should provide you with more info.