Unmetered Electricity Supply problem - HELP URGENTLY REQUESTED

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The flat is now let out on an AST but I recently received a letter from a neighbour saying that they had discovered that my electricity supply is connected to their meter and that they have been paying for my supply for years including for the previous owner.

They are now demanding that I come to an immediate settlement both for past supplies and current supplies until an independent meter is fitted or they will cut off the supply to my flat.

This is a terrible situation as I don't know what would happen if the supply was cut off given that the flat is tenanted and the flat is all electric.

My questions are as follows:

Do my neighbours have the right to cut off the supply and what damages might this leave me open to with regard to my tenant?

Do I have a legal liability to compensate them for past supplies?

If I am responsible for past supplies how can I arrive at a suitable sum? Is there a time limit of 6 years back responsibility? Bearing in mind that I have only owned the flat for 2 years am I responsible for any usage by the previous owner.

Any helpful advice appreciated