Firstly if they haven't billed you properly since 2015" they can only bill you for last twelve months, that should get more than half back. The industry term is back billing.
Secondly if there has been no meter read in that time by them, they are in breach of their licence which stipulates once a year min.
Thirdly if they have incorrectly reviewed your direct debit using estimates it is also a service agreement breach.
Thirdly they may have cocked up the night and day readings. In the morning look at the meters later on in the day, maybe after using kettles and microwaves and see which is the day rate meter. Check on bill, but be cautious if it's in your favour ie you currently have most use at night on the bill and its wrong, then it would be better not to rock the boat on this.
At the end of all that, they cant insist on immediate payment if it's do high, ask for it to be calculated over 24 months on your dd.
Check meter reads first and go from there.
For the record, on a flat like how you describe I would expect your current dd to be reasonable. Check the tariff you are on too, but don't agree a new one until after you've resolved all the above as that would lock you in to them. You can always insist it's backdated.
Also ask the operator to look through notes to see when you last had a conversation about tariffs. If you were advised incorrectly, then that can add to your negotiation.
Try all that first, and say 'i am making a complaint' to get the clock ticking for ombudsman. That will cost them £400 or so, so it focusses attention nicely.
Hth