Being pursued for energy bills at an address I've never lived at - England

I am currently being pursued for an unpaid energy bill for an address that I've never lived, which I was first made aware of in August of last year when a debt collection agency sent a letter to my current address. The address they're demanding payment for is next door to the address I used to live in.

In August last year, I received a notification from the debt collection agency LCS advising that I owed £649.59 for an energy account with Octopus at an address in London I'll call Address A, for the period 30/06/2023 - 11/09/2024. I have lived at my current address in Manchester since 20/10/2021 (with Octopus as my energy supplier) and have never been resident at Address A. However, before I moved here in 2021 I lived at the address next door to Address A, which I'll call Address B. Addresses A and B are both in the same building, which is administered by a dodgy landlord company. In a separate issue, I had been led to believe that the rent I was paying to this company was inclusive of energy bills - which turns out to not be the case. I am now on a repayment plan for over £3k of unpaid energy bills to Scottish Power for Address B. I only mention this in case someone thinks it's relevant, as I think this is a separate issue.

I informed LCS in August of last year that I had never been resident at Address A, and gave them proof of my address for the entire duration of the time period in question. They demanded further proof in the form of council tax bills which I did not have, but I got a letter from my local council confirming I'd been paying council tax at my current address for this full period, and they bounced it back to Octopus. Octopus then also contacted me demanding the same proof, which I provided, and I had heard nothing further about it since September of last year until last month.

Last month, at my current address, I received a new demand for payment from LCS for the same thing. I called them and they advised that Octopus had sent it back to them and that they (LCS) were unable to accept the proof that I'd given them last year since Octopus had sent it back, and that I would have to take it up with them.

I contacted Octopus immediately, lodged a complaint, and provided the proof that they asked for (proof of address for the duration again), and also pointed out that Octopus are my current energy supplier and have been since 2021 at my Manchester address. While the telephone operative was genuinely really good, they had to refer it internally as it was above the ability of the operative to deal with. That was more than 3 weeks ago; the operative has emailed me several times since to say that they are chasing it without success. I have today emailed to ask to escalate my complaint but given we're going into the weekend I absolutely won't hear back for at least a few days- probably longer given the track record but hey hoo.

I've come home from work today to find a formal demand of payment from LCS. I have given proof, multiple times, to LCS and Octopus that I have never lived at the address in question and has been resident in Manchester for years before the London-based bill is meant to have been accrued. This is stressful, is now listed on my credit report as a recent default, and I just want everything to go away. I have no idea how Octopus have been given my details as being associated with Address A and they have not told me.

Is there anything I can do to get them to drop this, or any other advice for me here?