go and find a bank that will give you the overdraft
then go into the branch and ask to speak to their manager and explain that bank x has agree'd to give you a much larger over draft facility and that you would like a cheque for the full amount of your bank account to be written so that you can put the money into the new account

don't close the account as they'll still be spending omney sending you letters etc telling you you've got a balance of £0.00p