OK, my expectation for milder weather around 20th is defunct. We will stay with the cool/cold weather, and it will often be unsettled.
On the plus side, Friday, Saturday and Sunday should stay dry and there will be some sunshine. There is though a chance of some heavy rain/snow developing either late on Saturday or Sunday – but only a chance. The nights will be noticeably cold with a good frost (unless it rains/snows).
For next week, expect a fair amount of rain. Or snow? Rain is the most likely outcome for Berkshire where I live, but some parts of England will get snow. It could feasibly happen any day.
Equally there is the potential of a milder day or two in the middle of the week, say 10’C.
I expect this cool and wet pattern to continue until the end of February, perhaps March.