What shorts or bibtights do you wear now, that would probably be a good place to start.
For me, I love the Progetto X2 pad in the higher end Castelli range - Merlin have this one at nearly 50% off, and only a tenner over your budget, but the warmth might not be what you are after, as it mentions 4-16 for temps, so depends on how much you feel the cold I guess:
Unlimited bibtights
I don't own these, as these are a recent model I think, I own the Sorpasso tights that have no pocket, as it wasn't a thing back then - I do find the side pocket/s really useful though on the shorts I have them on though.
Might be worth having a look at Lusso, as I think they had a sale and possibly an extra discount on recently.
Now isn't generally the time to find winter bargains, so might be best to stick it out, find what you want to buy, and then look to get them in March/April on sale ready for next year.