He had his brake pads replaced and the guy (mechanic friend) changing them said one of his discs had worn so changed that as well.

Are you saying only one brake disc was changed?

It's been reported that it's possible for a brake pipe to collapse internally, effectively making it a non-return valve. Worthy of investigation?

I'd certainly jack it up to see which corner was binding and concentrate my effort there.

I've just re-read this after thinking that it's one of these new Ford Ka thingies which are really a Fiat 500!

As it's a 1998 Ka (were they really making them so long ago?) you have done very well to keep it running for so long. Now a binding disc brake, at that age? I would suggest that it has to be a wear lip inside the cylinder. You've changed everything else... Bite the bullet and fit two new calipers and get a few more years out of it!

Are you ABSOLUTELY SURE that the flexi pipes were changed? DO they look new with nice shiney metal connections at each end?

If so many parts have been changed i have 3 suggestions:

1. what make of pads were used? Cheap ones? I've come across cheap pads where the quality of the baking plate pressing was so poor they had burrs and the plate was over size in critical moving areas by enough fractions of a mm that they wouldn't move freely. Make absolutley certain that the pads are free to move in their sliders.

2. debris in a pipeline somewhere? I'm guessing this car does not have ABS given it's age. I would disconnect the brake lines at the caliper input port and pressure bleed some fluid through. Reconnect and repeat from the bleed nipple
Assuming it's a non ABS model, you could disconnect the pipes at the master cylinder and blow them through from an airline

3. you could check that fluid is free to flow both ways by putting a set of worn pads back in (temporarily) or a piece of wood and pump the pistons out. Now use a wind back tool to make sure the piston can be returned ok and that the fluid flows in reverse ok. DO NOT DO THIS IF THE CAR HAS ABS.