Free Traffic Legal Advice

What can I expect to come from the council now? Court summons?

No, this is not a criminal matter, there is an enforcement process defined in law and regulations. If the council refuse all representations, you can take them to the adjudicators, (in your case, London Tribunals), to hear your appeal. If you lose that is the end of the matter, and the penalty must them be paid, but there are no additional costs to pay. Some cases in the past have gone a bit further to Judicial Review, but not many due to the costs involved. Of course, if you win there is nothing to pay.

I’ve just had the “rejection of representations” letter land on the doormat. There is an appeal form for the Parking Adjudicator enclosed.
Should I take photos and upload them here?

Yes, please, we need to see their letter rejecting your reps.

No re-offer of the discount so a no-brainer to take them to London Tribunals, but would you win ? On the contravention itself, I don't think so having looked at their photo, which shows your nearside wheels the other side of the bay divider. This is more than just "slightly over the line". Of course there may be technical appeal grounds. 

Thanks. I’d like to know what user cp8759 https://www.ftla.uk/index.php?action=profile;u=1 thinks, as he seemed to have a different opinion further up in the thread.

Well he may have seen a way ahead based on no notice about parking within bay markings near to the bay. Yes this can win an adjudication.

We saw one photo of a sign.

IMO, a tad risky to assume this is the totality of signs in the car park. The OP did not say this was the case.