That cotton is a killer sentiment is about right. Avoid it at any cost. Apart from anything it is hellish uncomfortable, pulls around all over the place, can get your tackle in a knot and will give you a rash if you are prone. Wide berth. If you get it wet sweating with exertion and then stop, you will stay wet, get cold and that can knock you on the head.
Wool is great. Go online and look. You want a weight of about 100, then layer. Smartwool do a great one at that weight and lighter, as do Woolpower. Not pretending they are cheap though. Peter Storm do cheap merino. Synthetic wicking t-shirts and longs now range from super affordable to super expensive. For a quick start, go to a sport shop and look for cheap running shirts/leggings in an artificial fibre. If you have cash look for light polartec for cooler weather
Rab and other companies have been experimenting this and last year with very long fibre synthetics which put the fluffy side of a fleece right against your skin. I guess following Woolpower's example. The US army has picked this up too. I might well give it a go when the prices tip my way a bit more.
I have a ton of this sort of stuff ranging from the cheapo sports stuff to Smartwool and Arcteryx gear. Winter and shoulder season camping includes fine powdery dry snow and heavy wet stuff, so one needs a few options. For a happy medium, the best bet would be to find whatever the equivalent of REI or MEC is in the UK .. Decathalon still going? ... and see what they have.
Ron Hill Tracksters are good longs ...cut them to about 3/4 length.Twenty seven quid. They have a long sleeve wicking tee for twenty three quid.
Have a look at Millets
https://www.millets.co.uk/mens/mens-clothing/baselayers/
..... huh! that link doesn't work so do a search on 'Millets Men's Thermals and Baselayer' lots of useful things
As mentioned, the big benefit of wool is tyhat you can go a few days without changing. Synthetics pong outrageously ... though there are some more expensive antibacterial ones now