Yes you can (typically about £1-£2), but depending on your fax set up, it can cause problems (e.g. the fax answers before you do, or you answer the phone and get a fax tone because someone is trying to fax you) Even bigger problems if you have an answerphone connected.
You used to be able to get a device called a fax-friend produced by Avro-Pacific that used to auto switch if required on answerphone, or allowed you to manually switch if you inadvertantly picked up a fax call.
Unfortunately Avro-Pacific went out of business some time ago and I don't know of any similar products. You can still find the fax friend by googling, but of course you won't get any support in case of difficulties.