you need someone to represent you by applying for what is known as a "Lasting Power of Attorney".
This costs around £150 and needs to be arranged through a solicitor.
You also need to check with your local county court to see where your bankruptcy petition must be taken. As you cannot do it in person and a 3rd party is involved it may be the High Court in London but check with the court first.
Which is your nearest county court? We may be able to give some advice regarding options there.
Also had the pleasure of helping a wheelchair bound gentleman in June at the High Court. I arranged special parking inside the court compound and it was all remarkable easy.
The LPa is as John says £150 to register but will probably cost £x for a solicitor to do it. The helpline may be able to recommend someone a lot cheaper and if you have no joy there I can certainly point you in the right direction
Paul Johns Assisted Bankruptcy Specialists Reviva UK