So you won't be getting a disqualification, you will be getting your licence revoked (totally different process). Which will require you retake both parts of the driving test again.
If you accept the inevitable fixed penalty, the DVLA will soon after revoke your licence. You could take it court, plead not guilty and defend the charge, but it seems very unlikely you would be successful based on the compelling evidence. Likewise persuading the court to not endorse your licence or to award you a short driving ban is a very unlikely outcome. Unlikely a solicitor will be able to influence the outcome either.
Can't see any way out of your licence being revoked.