Ok, Front discs and pads changed, fluid also changed.

Since then, I've been having an issue with the brakes, in that when I first press the pedal, the car brakes normally, however, if I come to rest, then the pedal will slowly sink to the floor. If I pump it, it immediately becomes solid, as I'd expect, but if I keep on the pressure, it will again, slowly sink to the floor.

Brake lines have all been bled again, no air. I don't appear to be losing fluid.

What could be going on please?

Did you ever do the same "test" previously ?If yes, was it the same ?

Superficially, the result indicates that the mastercylinder is leaking internally, across 1 of the high pressure seals.
Assuming it was ok previously, most likely is that bleeding disturbed some dirt / debris & it's now lodged on the outer lip of one of the main pressure seals. Alternatively, full stroke during bleeding has damaged 1 of the seal lips when it moved into an area of the bore not normally used.
If you're very lucky & it's the former, you might be able to 'wash" it off by pressing the brake down & releasing it fast a few times or by pressure bleeding with the brake pedal held partially down.
If it's the latter, it's time for a new mastercylinder. Paul,
2001 Discovery 2 TD5, 211,000 miles & climbing
2006 FFRR TDV8 Vogue 151,000 miles & now sold
Member of Midland (Land) Rover Owners Club, www.mroc.co.uk

I presume your ff is diesel ?
If it is this is normal and is known as diesel creep something to do with the air intake or something
If your car stops normally and you can hold the car on light pedal pressure then it's fine if the pedal goes hard on switching off then that's ok
Do a search on diesel creep to set your mind at rest

^+1 for diesel creep.

And we have a winner!

This is exactly what I am experiencing. Well, well. I had never noticed before. I think that, as I had changed the discs and pads on the front, and also changed all the brake fluid, I just automatically suspected that I'd done something wrong, or broken something in the process. I re-bled the brakes twice, assuming that I had got air into the system.

Yes, I can hold the car on light pressure, and the pedal is rock hard when switched off.

I've even just gone to my wife's 3.0d X3, and it does exactly the same thing. Probably not quite to the floor, but very close.

Thank you so much, looks like I did the job right then.

That's what I love about RR ownership, there's always someone who knows what's going on.

Thanks again

Ummm, what if you were descending a long steep hill with a caravan on the back - what happens when the pedal hits the floor? You have to keep pumping the pedal?

Only happens at idle