+1.
OP, this is a two-part debt and requires a two-pronged approach.
1. The council's penalty charge of £204. As per others, too late.
2. The enforcement agent's fees of £310. They are required to serve mandatory notices on the debtor. The first is a Notice of Enforcement for which a fee of £75 is chargeable. The NoE must give you 7 clear days in which to pay the debt at that stage.
There are regulations and national standards which sit outside 'parking' and IMO you should seek to engage with these.
But not on your own, I suggest you contact bailiffadviceonline or other reputable person for this detailed advice and support. A fee is charged, but <<<£310 which you've already paid.
And remember, the enforcement agent is an agent of the council.