I think you will find that turf grows in every area of the country.
Go to any B&Q and buy a roll of artificial and while you are sitting in the sun you can shout 'mower wanker' over the fence to your neighbours.
I thought the idea was to get the whole lawn looking good not just areas of it.
I would ask for my money back.
The answer to the OP is to lay artificial grass or do a Fred West and pave it over.
The Brits and their bloody lawns make me laugh, what you going to do play bowls on it or something...