YOu will need to obtain a Lasting Power of Attorney from the Office of the Public Guardian where you appoint a representative to act for you .
The LPA costs £150 to register and once granted - 3 to 6 months - then the representative can apply for bankruptcy for you at the High Court in London.
This costs a further £522.
Costs for representation vary from free for a friend to £3000 for the last solicitors quote I saw.
There are other professionals that can represent you for considerably less!