Free Traffic Legal Advice

To advise we'll obviously need to see your defence, and the particulars of claim to which you were responding.

Likewise any background to the case and any pre action correspondence (incl. Initial notices, any appeals etc.).

This might not be the case, but from the wording of that strike out order, it seems you may have copied and pasted someone else's defence rather than writing one that specifically responds to the claim.

We need the background to this, your story and the original Notice to Keeper, if you want help with the construction of a defence deemed more acceptable and appropriate to your circumstances.
Your problem seems to be that your original defence was copied from here, and may be applicable, but is vague and not specific to your circumstances.
It’s always the problem with “templates” which some people seem to demand. In your case it looks like you did some research first.

It is certainly true that the Particulars of Claim are woeful and do not meet the requirements of the pre-action protocols. But in this case the court has decided that this point is not sufficient for a defence.

That appears to be a covering letter from the courts, not a Notice to Keeper.

Your defence needs to be a story relating why the driver is not liable, in the face of claims that the driver read the terms clearly indicated by signs and accepted them and entered into a contract by parking.
Why is the contract invalid, or the driver not liable?
In the absence of a notice to keeper, you can request a copy but not necessarily in time to construct a defence around it. Look up Subject Access Request if you want to try. You won’t get a response within 9 days, by 12 May as required.

Hi,

If I can't get this information in time, what are my options?

You need to write and submit a defence. If you want to, post it here before the deadline (4pm on 12 May) you may get input to improve it. It’s your defence and your story.

Remember that the claim will be against you as the registered keeper for actions committed by the driver originally. If the driver is not identified, they may be unable to transfer liability to you. But without the original NtK this will be a harder case to make.