It is not "pavement parking" that was banned in the 70s in London. The ban was on parking "off the carriageway", a key difference, and looking at your photos, I'm puzzled that you managed to get away with parking there for so long. In addition, despite the 70s legislation, you are also parking contrary to the double-yellow lines that apply to footways and verges, not just the carriageway.

No TMO is needed to enforce the 70s ban, it is an Act of Parliament, and nothing more is needed.

If enforcement is only recent , it looks as if somebody has made a complaint, or a "new broom" charged with bringing in more PCN cash, has taken over.

They should have sent you a postal PCN.  You seem to have missed receiving this, so as time went on the period to respond to the PCN expired, so they have served a Charge Certificate.
I suggest you get onto them straightaway, because it is my understanding there is no facility to submit a witness statement in Scottish law, unlike England.

Well, two things.
1.Their photos do not show you passing any restriction sign.
2.Please post a GSV link to the exact location on Vicar Lane.

As this case hinges on signage, we really do need to see those signs. Sorry if this means you've got to trek out there again. At t he moment all I see is the geographic layout sign at the junction showing a No Right Turn symbol on the right. You can just about make it out in their first photo. I think that is totally inadequate, but you have to accept you'll have to forego the discount and take them to the TPT.

First off, DO NOT PAY the Charge Certificate.

 It is essentially an unlawful demand for money when the appeal process is taking place, (London Tribunals in April 2027).  The date of the CC is probably sufficiently close to when you registered the appeal that it won't be your Get-out-of-Jail-Free card, but it could do. It depends on when the council received notice of your appeal date.

I suggest you contact the council to state that you registered an appeal at London Tribunals on <date>,  which was before they served a CC, and demand that the CC be cancelled forthwith, or you will include this unlawful act in your representations to the adjudicator.  Appeals have been won exclusively on this aspect many times before.

Frankly, you have correctly identified the issue, which is the absence of an arrow on the pay-parking sign misled you to think that provided one paid, one could park all along the bay. You assumed that the sign for Business Permit holders meant that they could only park for free to the left of the arrow indicating where they could park, and not to the right, where they would have to pay just like other motorists.
That seems a reasonable argument to me, to take to London Tribunals, but you have to risk the full PCN penalty, of course.  There are no additional costs if you do so, only the penalty if you lose, and if you win you pay nothing. The council don't get away cost free as they must pay the adjudication fee, and also tghe PITA of preparing an evidence pack.

So its your call now.

There's clearly some mistake here. I only have 1 PCN and made representations. No one in my house was near the Blackwall Tunnel on the 17/8.
What do i do from here?

EDITED TO ADD:  I've just checked the TfL bounce back to my representation and it has the wrong reference on it.  Not the one I would have typed in, that's stated on my PCN.  I couldn't have guessed a completely different number and one that actually matched a ticket they issued a few days before.

I just went onto the TfL website and typed in the number and it's still showing as £90 and that I can still make a representation.

I'm very confused!

and presumably the same registration number for the car ?

TE7 and TE9 are not required to be witnessed. Only the Statutory Declaration used for London-specific traffic legislation needs witnessing.