In many areas of the UK, the National Health Service (NHS) makes provision for the supply of wigs or hair pieces to cancer and dermatology patients who need them.
In order to qualify you need to have a referral from the hospital where you are being treated or you can speak to your GP and ask to be referred. If you have a condition that you are unable to cover up easily (some have specified at least 50% hair loss) then you should qualify for a wig or hair piece on the NHS.
It is up to your consultant to decide if you qualify for an NHS prescription. Some NHS Trusts provide patients with a choice of supplier, some will only provide you with the option of one.