Even if you managed to convince the energy company to only bill you from Jan 2017, it is highly unlikely you will be able to get away with not paying for the energy which you yourself admit you have used over 3 years. The old occupier can quite easily make a claim against you directly for these costs so in the end, one way or another, you will likely have to pay that. Generally, you cannot rely on the law for your own personal benefit, especially when it is clear that it is clearly not equitable or reasonable, as in this case.
I'm sorry if this is not necessarily the answer you were hoping for, however I do have a duty to be honest and explain the actual legal position. This does mean delivering bad news from time to time. I hope you understand and would be happy to provide any further clarification if needed. If you are still satisfied with the level of service I have provided regardless of the contents of the answer, I would be grateful if you could please take a second to leave a positive rating by selecting 3, 4 or 5 stars above. Thank you