Didn't Indigo get your address when you first appealed? In which case they wouldn't have needed to go to the DVLA - they could have simply passed the whole file over to Debt Recovery and Prosecution Services (DRPS).
DRPS is actually an alias for Southeastern. I guess the letter you got from them looks something like this (taken from Torino's recent thread):-
https://imgur.com/a/No6fY00 . The letter is full of flaws, but most importantly, the assertion that you are liable for their "penalty" is fraudulent.
It is a fundamental principle of our criminal justice system that everyone accused of an offence is deemed innocent until proven guilty. This means that no-one - not even a train company - can compel you to pay a penalty for parking in breach of the Byelaws before the alleged offence has been proved. Only the Magistrates’ Court can impose a penalty, and that’s only when the motorist has either pleaded or been found guilty. This was specifically confirmed in a letter from the Department for Transport dated 18th February 2016, here:
https://www.whatdotheyknow.com/request/311011/response/770331/attach/2/F0013227%20Follow%20Up%20Reply.pdf?cookie_passthro ugh=1
It states:
“…no other person or body other than the Court is able to impose a penalty for breach of the Byelaws [including Byelaw 14 (1-3)] made under Section 219 of the Transport Act 2000 (as amended) and made operational on 7 July 2005.”
Your case is a classic example of why the presumption of innocence is so important: you've done nothing wrong. So let them try and prove otherwise (they won't). Don't even think of paying. Report the matter to your MP, and remind him about Article 6 of the European Convention on Human Rights.
It's high time our elected representatives did something about these Big Bullies who act as if they are above the law.