I recently visited my most local sites of Gorse (Ulex europaeus), as recorded on NatureSpot, at Howell Nature Reserve and the solar power installation between Asfordby, Saxlebye and Ab Kettleby, but found no Gorse present. However, there was abundant Birdsfoot Trefoil (Lotus corniculatus) in these locations. They're both of the Fabaceae/Leguminosae familiy and have very similar flowers, so I suspect these records may be the result of mis-identification from photographs.
I'd be surprised if there are many Naturespot recorders who would mistake bird's foot trefoil for gorse and I'm confident it wouldn't slip past the verifiers. (I'm not one.) If you go to the Explore All Records tab (available when you are signed in) you can filter to see the records of interest to you. Most of the ones you mention have associated photos, which clearly do show gorse.
If you find an answer to why gorse flowers in winter, let us know!
All records submitted to NatureSpot are verified by experts. Holwell is a big reserve and there certainly is Gorse there, I've seen it.