Hi Tony, your body will be in UK winter mode, you will be fine all day, everywhere. I was in Barcelona last week, it was 15c and raining, anything more than a T-Shirt on had me sweating as I rode around..
Barcelona is near the coast and low altitude, though, so it will be warmer than the high altitude areas in the middle of the country. Also, if you were in the sun, 15C and sunny is very different from 15C in the shade. There's still a lot of heat in the sun here, even in winter, and it's deceptive, as we've found out through living here.
Take a look at the current forecasts (late November) for
Leon or
Salamanca, for example (both on Pedro's route). They're showing night temperatures of around or below freezing, and daytime temperatures barely out of single figures. When we drove down across the middle of Spain 3 years ago, in the middle of October, the temperature at 9am when we left our overnight stop near Burgos was 2C. Even for someone acclimatised to the UK, it was cold!
You also have to be aware that Spain can get "cold snaps". Two years ago, we had a few days of 0-5C at the beginning of December, right down here on the southern coast.
I'm not suggesting the trip is a bad idea, but getting caught out by cold and/or wet weather when you're not prepared for it is a very miserable experience.