The National Archives does not hold these records yet. The 2000 index is being prepared for transfer. You need to contact the Royal Courts of Justice at:
Royal Courts of Justice Room 81 Strand London, WC2 A 2LL
Tel: +44 (0) 207 947 6224 or 6656
Newspapers
Many people who changed their names didn't want to draw attention to it. It is unlikely that you will be able to find proof, but it may be worth looking through local newspapers. You could try contacting your local library to see what newspapers they archive. The Familia website can also help you find what is available.