Nick Thomas
... I think am right to assume there were no spoilers...
Correct.
...so on landing did the act of bring the nose down spoil the lift...
Yes, as with most conventional aircraft, reducing the aircraft pitch attitude (once the main wheels were on the runway) would reduce the angle-of-attack and therefore reduce the amount of lift being generated by the wing. Modern aircraft wings are very efficient and will still be generating a considerable amount of lift during the landing roll, even as the aircraft slows down.
Put simply, spoilers and/or lift dump systems are required to destroy this lift, in order to get as much of the aircraft weight as possible on the main landing gear, which, in turn, allows greater pressure to be applied to the wheel brakes before the wheels start to lock-up and the anti-skid units activate to release the applied brake pressure.
Concorde’s wing however developed very little lift at zero pitch attitude, so, once you had landed the nose wheel, there was no need for spoilers.
...is that the reason why the non flying pilot pushed the yolk forward once she was down?...
No.
The reason was that using reverse thrust on the ground on Concorde caused a nose-up pitch tendency, strong enough to lift the nose. The procedure was the handling pilot would call Stick Forward as soon as she had landed the nose wheel and the NHP would apply forward pressure on the control column to make sure the nose didn’t rise.
If the handling pilot applied reverse thrust before the nose wheel was on the ground, things could get very awkward very quickly.
Firstly, the nose would probably rise, quite possibly beyond the power of the control column to lower it. Secondly, the wing would still be generating (some) lift and so only reduced wheel braking would be available before the anti-skids kicked in, and the amount of runway left would be diminishing faster than normal.
The solution was to reduce to Reverse Idle power until the nose wheel was back on the runway, however, in the heat of the moment it was very easy to go through Reverse Idle and on into Forward Idle. Not only would this again hinder the deceleration of the aircraft, but it would also run the risk of scraping the reverser buckets on the runway (as the buckets moved from the reverse thrust position to the forward thrust position) so tight were the clearances between the buckets and the runway on landing.
Best Regards
Bellerophon