Have you tried cutting a square of turf out to see if anythings going on beneath, like mycelium spores, if so the soil will appear to be very dry and crumbly with white spores, have you had problems with fairy rings in the past ? sometimes this can form into big large areas and not as i the usual fairy rings, also could the problem be bitch burn, any dogs coming into your garden ? what about chaffer grubs ?

No fairy rings, in fact no fungi at all as far as I've noticed. I will try digging up a bit and having a look. I haven't seen any dogs, and the patches are much too big for urine spray anyway. I'm really hoping it isn't going to be a case of digging it all up and starting again! Would chafer grubs make large patches?

It could be Brown Patch Disease (Rhizoctonia Fungi).

What's that, and more to the point how do you tell and what do you do about it? I dug up a couple of turfs from different places today and no sign of the symptoms Julien suggested. The roots didn't look good though, no nice white ones at all, just thin little brown ones.

I looked it up for you and was able to find this:

Brown patch, caused by Rhizoctonia solani, is a disease of cool-season grasses, including bentgrasses, bluegrasses, fescues, and ryegrasses. Brown patch commonly occurs during periods of warm and humid weather. As the name implies, gross symptoms of brown patch are brown or tan patches of diseased turf ranging in diameter from 5 cm (2 in.) up to 1 m (3 ft) or more in diameter. When close-cut turf (<2.5 cm or 1 in.) is wet, brown patches are often surrounded by a dark brown or gray ring called a "smoke ring". The smoke ring is evidence of active fungal growth on the turf foliage and is an initial sign of brown patch development. Brown patch typically does not result in damage to all tillers within a developing patch, therefore, the turf may recover when disease pressure is reduced by change in weather conditions or implementation of control practices.

That's helpful Myron, thank you. I wonder what they mean by control practices.I'll google around and see if there is any more info. If it doesn't recover I guess its just a matter of reseeding but as the lawns were turfed before we came here I've no idea what sort of seed will match.
Not all the patches are round, some are long - quite a variety of shapes actually.