No you don't.
If you didn't realise that this was the situation and you bought the property believing it had vehicular access, go back to the solicitor who assisted in the sale of your purchase.
It is a standard question to check as part of the solicitor's work. Ask him/her why this did not crop up. Depending on the answer, you may have a claim against the solicitor for negligence, but it won't help you get an access.
The only way to get access is by buying back a strip at a price the owner can determine. It's not called a 'ransom strip' for nothing.