Of course! I'd strongly avoid anything that contains cotton, as it absorbs water, feels cold and clingy when wet & doesn't dry out.
My recommendation for UK caving is a Polypropylene (PP) based thermal, such as the Helly Hansen Lifa stripe 'Stay Dry' range (~?20-25 for a top). Check Amazon / eBay for cheap sellers. You want your thermals to be a close fit, practically a second skin with no room for the 'bellows' effect.
Merino wool based ones are warmer, but they're probably too warm for summer caving in the UK, dry very slowly, and are heavy when wet (though supposedly, still warm when wet, but that sounds like rubbish to me... I'd say more just 'less cold' than equivalent cotton! PP tops literally dry off your body). Though if you're dry caving somewhere it's cold, they're ace. They're also exceptionally comfortable for winter mountaineering, biking in the cold and lazing round chilly caving huts. They also don't stink, whereas once you sweat a bit in a PP top, it will never quite smell 'right' no matter how much you launder.
Tops are far more important than long johns, I usually go to wearing 2x tops (often a short-sleave one, and a long sleave one) before wearing a long john.
A good budget option is the 'HEATTECH' stuff from Uniqlo if you have a store near you. These are often 2-for-the-price-of-1, and though not as nice as a HH top, if you find the design without cotton (again, check the label), they're ace. The turtle neck designs are particularly toasty, but a rather strange fashion statement when you're not underground!