"Its a more or less open plan flat so unless I have lead in the walls or something silly like that stopping the signal... I don't know!"
Actually, some modern buildings do have sheets of aluminium foil in the walls for thermal insulation and this will kill WiFi signals.
Although it is possible to use wireless routers as Wireless Access Points, they would still have to be interconnected with ethernet cables, so this won't get you much further forward.
A possible solution would be to use Homeplugs which network via the mains electricity supply. There are "wireless" ones which could be used in the rooms where you need wireless access.