I would telephone TEC. Northampton County Court Bulk Centre, otherwise known as TEC.
As you say the council has refused parking permits etc and if you can prove that you live in the area and are entitled to it, then they have a case to answer.
The phone number for TEC is -
0845 7045007
The Council obviously appear unreasonable and you have a right to contest the fine being with Bailiffs if you have already tried to negotiate with the local authority.
TEC states -
If you wish to appeal against the registration with the Court
If a correctly completed Statutory Declaration is filed with the TEC within 36 days of registration, the Court registration will be revoked (cancelled). This does not cancel the original penalty charge. The matter is referred back to the local authority to decide what action they wish to take next.
They will then get you to fill out a stat dec -
Traffic Enforcement Centre
It will suspend the warrant and force the local authority that gave you the ticket to answer to a court why they allowed it to go to bailiffs and answer why you are not entitled to a permit.
The process suspends the warrant - you can in the meantime, save for the extra bit to be paid! you have about 14 days - 21 days from the date TEC accept this.
Good luck!