Ex-BH, on his hill farm in north Cumbria, used to leave a tup running with one batch of ewes year round, just to see when the earliest lambs would appear.
The ewes were mainly Texel and Beltex crosses, with North of England Mules in their ancestry, and a handful of Lleyns.
Up until he got a Charollais tup, the earliest lambs were usually mid to late February. Once he had a single lamb on Jan 4th, and once a ewe lambed on Jan 31st.
Once the Charollais blood started to be in the breeding ewes, however, the ewes would start to cycle much earlier, so he had to keep the tups separate from August onwards.
The tups were January born themselves - I don’t know if that made a difference.
My own flock, a mixture of mostly rare breed and primitive cross breeds, used to run with the Shetland tup year round on that same farm, and I never got lambs before late March.