Some banks are pretty thick. If you are paying UK national insurance on income earned abroad but where that money is paid by a UK employer and it is also taxed by the UK, it is a pretty good signal that you are still considered as a UK resident!!! My husband is in exactly that situation, he was told by his bank that he no longer qualified for an ISA, but he does indeed qualify for an ISA, HM Revenue and Customs treat him as if he is physically in the UK, so therefore all banks should treat him the same - I would refer any mortgage providers that refuse you a mortgage simply that you are not currently in the UK to HM Revenue and Customs - if you are obliged to pay UK tax AND crucially UK national insurance on a UK salary, you ARE still a UK resident. Very few people are in this situation, I can think of UK crown servants and UK Armed Forces personnel posted outside the UK as being the 2 main categories of people who are in this situation.
I would however be a bit cautious about going for a mortgage immediately as a "buy to let" as you will be charged less favourable interest rates. Plus you might actually not make enough profit on the rent to cover the cost of the mortgage and maintenance costs. We have a mortgage on our UK property still and the income from the rent would in no way cover the cost of a 90% mortgage on that property, even though we are charged an interest rate as if we are living there and we only get that interest rate because it used to be our family home, otherwise we would be paying 2-3% higher on a buy to let interest rate. You do also have to consider Capital Gains Tax if you ever end up selling. The UK tax regime on rented property is not great - out of £600 rent we receive on our UK house each month, we end up with maybe half that amount after we have paid maintenance costs and tax, so we make less than £4000 a year on a house which has a value of around £225,000, it's a very low rate of return, if we had that amount of money in the bank, we could instead be making over £8000 in interest!!!! Yes maybe it's time to think about trying to sell our house again.