We also had higher vaccine uptake than many European countries and were well ahead on boosters going into Omicron
Not Denmark for sure, on either level, although boosters is an interesting one, as boosters are very much waning for protection against symptomatic omicron, so being early on boosters may not be an advantage in spread, but Denmark is on about 105% doses, to our 100% doses and is doing it twice as fast currently.
On protection from past infection - we don't have reliable data because we still don't have re-infections published in London particularly where it would be useful - However, we do have re-infections included in the welsh data, if re-infections were significant, we'd see Welsh data being much higher than England. (Unless of course the different NPI's in Wales happened to reverse it, despite those same NPI's doing nothing in European countries)
The imperial estimate particularly looks dubiously ineffective, given other estimates in other countries data too but we don't know.