Yes, second had, but you’d be astonished how many people buy high end ski gear for their first time skiing, use it for a week, then jack it in. Most stuff is as new. I bought a Roxy jacket that retails at around€300 for €35. Used for one week, in pristine condition. Plus if it turns out she doesn’t like skiing, you can always sell on.
£150 won’t get you much new, unless it’s all Decathlon. You’ll need to buy a jacket, trousers, a snood, tops, gloves, socks at the very least. She can wear leggings under the trousers, no need for thermals, at least at beginner stage. Plus in recent years it not really been that cold. Helmets and goggles can be hired at the resort, alongside boots, although Decathlon do sell cheap goggles which are perfectly fine. I used mine for many years and only treated myself to more professional ones recently.
she’ll also need warm, waterproof footwear. Again decathlon have some ok very basic snow boots. I still use those, they’re totally fine. My ski boots are branded as they do need to fit well and be adapted to your level of expertise, but the apres ski stuff no.