I am female. You're doing the reverse of my 2019 trip, though mine was longer. It began on April 9 in Spain and reached Scotland (for 26 days) in July; in between Spain and Scotland I was in western France including potentially cool, damp Brittany. There were a couple of cold days (upper 30s in the AM) in northern Andalucía during the second week of April. It was not even close to that cold in Scotland, but I did get rained on a lot (though the east was a lot drier than the west). That's the weather gods for you.
I am extremely cold-natured and don't travel carry-on only. I packed/wore 3 pairs of slacks and 5 tops suitable for moderate-to-hot weather and added the following:
2 pairs of merino wool long john bottoms (used together 2x in Spain)
1 merino wool long john top
1 light fleece jacket
1 waterproof, hooded rain jacket/windbreaker
1 packable down jacket (never used)
2 pairs of merino wool socks in addition to regular socks
waterproof shoes (no extra pair)
good-quality collapsible umbrella
The double long johns would have been overkill for anyone else and not worth the space, but I was glad to have them. They were not the same weight, so they provided an extra option for matching the weather. They were most useful on wet days, when they helped keep me dry. Just about every chilly day I encountered was also wet.
The most useful item in my suitcase (thanks to a suggestion from this forum) was a pair of 97% or 98% nylon slacks. Mine are by PrAna, but there are other sources, including Columbia. The Columbia version is not as heavy and seems to wrinkle more. Those slacks were somewhat water repellant (not totally waterproof) and kept me totally comfortable when worn with the merino long johns. On hot days they were about as comfortable as any slacks I've used in Europe. On my next trip I will take two pairs. On trips with appreciable time in sure-to-be-hot places, I like to have one pair of super-lightweight 100% cotton pants. I buy mine at street markets in Europe; they are approximately pajama-weight. I'm not sure they're any more comfortable than the PrAnas, though.
I think you'll be able to fit what you need in a carry-on bag. The reason I don't do that is that I have to take 4-1/2 months' worth of pills (6 lb.), and much of my voluminous travel literature is paper-based. I never have access to a washing machine; I sink wash. A compression cube or two will help.