How to convince council this is my main residence

jimmo

If I’ve got it right you are trying to establish that the Scottish property is your main home and London is your second home. In that way you will qualify for single occupancy discount in Scotland at 25% on both the Council Tax and Water rates (due to the Scottish system). That makes sense to me so I do hope it is right.
In any event, as you have a lodger in London you cannot claim the single occupancy discount. Also, I assume, you could not claim any second home discount in London because even if it is your second home, it is your lodger’s main home.
If that is the case I see what you are trying to achieve and wish you luck but I am afraid the taxman in me still sees London as your main home.
Onto the bit I do know something about which is nothing to do with your original question and you may have already considered it so please ignore me if I am just sticking my oar in.
Where you do own 2 homes at the same time it is probably a good idea to nominate the property bought second as your main home for some time. The most obvious benefit is that you ensure that both properties will be exempt from Capital Gains Tax for their final 3 years of your ownership. To achieve that there is no minimum period of nomination. You can nominate for 1 day and change your nomination the following day and you will still get the last 3 years of ownership.
Tax planning is not my strong subject, I was the gamekeeper, but I think, in financial terms, it is normally wiser for the property with the better potential for future growth (in value) to be nominated for the majority of the time. On the other hand if you do intend to move back to London when your job finishes and see yourself as continuing to live in the London house, maybe for the rest of your life then continuing the nomination of the Scottish property makes sense to me.
Now, what about the rental income you receive from your lodger?
If you are making normal Returns of your letting income then any rooms occupied exclusively by your lodger do not come within the normal PPR or main residence relief for Capital Gains Tax purposes. Lettings relief is available but will not necessarily cover the whole gain when you sell.
If you are using the “Rent a Room” scheme that only applies to your main home and, at the moment London is not your main home in your eyes.