I think the waxcap is
Hygrocybe acutoconica, which is the latest name for
H. persistens. Waxcaps are not thought to be ectomycorrhizal, so it will not have been actually growing with the rockrose. (Some researchers have postulated that some species of
Hygrocybe may be mycorrhizal with grass species but I have not seen this confirmed.)
The funnels in Christine and Chris's photos are are in the group with non-hygrophanous, somewhat velvety cap surfaces (technically the cap cuticle is a trichoderm) which are now placed in the genus
Infundibulicybe. This is a group which has all the classic problems that Chris hates for larger fungi in that the species seem to be separated at macroscopic level on nuances of colour, smell or other imprecise differences, while microscopic characters overlap considerably.
There seem to be only three options for the specimens in both sets of photos:
I. gibba,
I. costata or
I. squamulosa. Although these tend to be woodland species, they are saprobic, so there is no reason why they could not be found in this type of grassland. Dried specimens of
I. costata should show a brown reaction with 5% KOH, whereas the other two species would not.
I costata also tends to have a ribbed (or costate) margin to the cap (possible hints of this in Christine's photo?) and the stem colour tends to be darker, matching the cap colour. Christine's specimen also appears to show a somewhat scaly cap surface, possibly suggesting
I. squamulosa. So I don't think a definitive answer is possible from macroscopic appearance. Whether microscopy would help is also a moot question.
Ken