English winters are tricky for selecting winter tyres, the conditions vary around freezing every day. I only fit my winter tyres for a Big Freeze.
I bought some cheapo MTB tyres with big, well spaced knobbles and screwed some 3/8" panhead, self-tapping screws through the large knobbles, pointing out to the edge of the contact zone with the pavement, from the inside (20-30 per tyre). Dremel off the point to leave about 3mm and if you want, glue a patch of old inner tube over the panhead.
This costs less than £20/pair and takes about 2hrs labour per tyre.
Grip on slick black ice is excellent. Mine are on their 3rd winter.

They are heavier and less efficient than my usual slick Big Apples so they only get fitted if I really need them. On a heavy frost with occasional black ice, it is always a dilemma what to fit.
If you have spare wheels with winter tyres, the choice is made much easier. I have to use my set of wheels (Front dynamo hub and rear internal gear hub).