I mow it (regularly and not too short).
I weed & feed it (Evergreen complete).
I rake and fork it.
I water it.

And still it looks like this:
http://www.genesis-x.nildram.co.uk/images/dscf0041.jpg

Closer:
http://www.genesis-x.nildram.co.uk/images/dscf0043.jpg

Even closer:
http://www.genesis-x.nildram.co.uk/images/dscf0044.jpg

Even the best bits of the lawn still don't look that good:
http://www.genesis-x.nildram.co.uk/images/dscf0042.jpg

The size and shape of the grass stems has changed over the last couple of
years. They used to be dark green and very thin, but now they are thick
and flat; a lighter colour, and sort of horrible and gnarly. The whole
lawn is thinning out, with just these mutated stems growing in clumps.

Should I just give up, start again, and re-turf, or is there another way?

Have I been invaded by the dreaded couch grass? It doesn't have the same
long white root system, but it is just as ugly.

-
[H]omer