It's good to hear that you have made some progress with your situation, and that Tili now acknowledge that they messed up your switch.
Mistakes do happen, and I guess that you were just unlucky, Tili generally do have very good ratings:
https://uk.trustpilot.com/review/asktili.com
There again as we all know - if you want a job doing well then do it yourself.
And as the accounts are in your name then Tili be limited in what they can do now regarding refunds and the like.
Being practical to get things resolved -
Has OVO actually been charging you for usage? From what you say it sound as though they haven't.
So have you just been paying DD's to OVO that have now built up a £3k+ credit balance?
ie, What does your account balance at OVO say?
The answer to that could make a difference to what you have to do now.
(It OVO have been charging you for use then it wil be an ‘erroneous transfer of account’, if OVO haven’t been charging you then not).
I would also contact Utilita now and calmly and politely let them know what has happened, what is happening now, and that you will be paying them once you get the money back from OVO.
That should stop them escalating their outstanding billing to Debt Recovery action from a Debt Collection agency.
It might also be a good idea to make a gesture and set up a DD with Utilita now, one that doesn't yet include the debit repayment, to show them that you are willing to pay and just need time to sort the outstanding balance out.
As you have cancelled your Direct Debit to OVO then you should get an email asking you to set it up again and probably then a phone call asking the same thing, obviously you will decline and politely explain why not.
Whenever you have to deal with these kind of errors it is always best to hold your tongue no matter how angry you are.
Be calm and polite, it does get you a resolution much more quickly than shouting at people does.
Remember that they were not the ones who messed up, and they will be more willing to help sort things out again if they are not being shouted out.