Xiaomi Mi Band 3 is probably the best rated budget one, they’re about £30. I think Huawei do one for a similar price.
If you want more smart capability then I’d have a look at the Amazfit Bip – I have one of those, and it’s pretty actually good for the price. Mine was under £40, think they’re just north of £50 now. But that does steps, heartrate (not sure how much I’d trust it) as well as text messages, phone alerts etc. The battery also lasts for a genuine 30 days (I’ve had over 40 from mine with the HRM turned off, round about 30 with it on, using the GPS kills it a lot quicker) which is more or less unheard of.
That said, just using her phone isn’t a bad alternative. Plus if she uses Sweatcoin she can get free stuff.