The best way to keep in heat is to enclose the front door and the stairs.
But that would leave you with a room that feels long and thin.
Instead consider adding a vestibule by the front door and because that will make that part of the space narrower put the dining table there.

Thank you Jonathan, something like this ?

Or this?

Here's the planning drawing 7 years ago, when the room still had a dividing wall. The kitchen is big enough for a big dining table.

No.
I wouldn’t have the division between the front and back reception room. It sounds like they intend to use that back room most and if they divide the total space it will make the part they use feel smaller, it will make the back part of the living space, windowless, and since they are going to eat in the kitchen a separate front reception room could be redundant and unused.

What I would do

Thanks for those plans @Jonathan . Maybe a craft room office in one of the upstairs bedrooms. No worries about leaving out on show work in progress projects.

Would you put a door on the bottom of the stairs?

There's currently a radiator where the coat cupboard is, that could be made much smaller and help dry coats perhaps. The second radiator is on the stairwell wall behind the settee that faces the TV. Could add radiator cover. Maybe add a small radiator under the west window where the seating nook is.

Thank you