april1967:There is at least one mainstream lender who would consider this.
I would be very surprised if any lender including Halifax will do this as one of the main basic conditions for any residential mortgage with any lender is that the applicants (all of them) must use the mortgaged property as their main residence, if you start breaking from this then it is a short walk from here to renting residential properties.
What I will also add is that Halifax are not keen on anyone that does not pay UK tax on their income and even less keen if their main income is not paid into a UK bank account.
I am mortgage broker and live run my practice right on the border with Northern Ireland / Rep of Ireland and this is not the most unsual scenario as plenty of people work one side of the border and live the other and while lenders are accommodating to a certain extent I can say for certain is that Halifax do not like it if they cannot see UK tax being paid and in nearly every single case I have ever placed with them (I place lot with Halifax) they will insist that any earned income that pays tax (they generally do not accept many other forms of income) must be paid into UK bank account.
If the non UK resident also does not pass the credit check, they are a dead duck in the water too and this will likely be the first and biggest hurdle they need to beat