Ok - what you need to do is get a Solicitor to write and ask that it is processed within 7 days or say you will go to Court.
If they do not respond or refuse then you can seek a Judicial Review of their decision. This is where the High Court examines what they have done to see if it is reasonable and legal.
The Court can either agree with their decision or remit it back to be reconsidered.
But this is a drastic step but I know time is of the essence.
As such therefore this seems the quickest route to take. You could consider an injunction to make them process this faster, but for that you would also need a Solicitor to complete form N208:
For more information on Judicial Review please see:
Can I clarify anything for you about this today please?