I wear a baselayer under my jersey all the time.... even when it's over 100 degrees (F).

If it's colder, I wear a long sleeve thicker baselayer/jersey between my base layer and jersey. If it's really cold, I wear two layers in addition to the short sleeved base layer, and a long sleeve jersey. And a vest.

If its just cool in the morning or on a descent, a vest and arm warmers in addition to the base layer and ss jersey.

I find that it's important to have good zippers and sleeves that I can push up, so I can shed heat on climbs. You don't want to get all sweaty on a climb and then go down a descent, you'll get chilled.

I'd recommend you buy at least one of all of those and more than one base layer and jersey. And since you're in the UK you'll need a good rain jacket too.