One of the least expensive monitors is the Xiaomi Mi Band 2 - just over twenty quid. Got one to dip my toe in the water - and really am quite impressed.
Good battery life. Seems to perform OK within its capacity. Has what seems an effective heart rate measuring device. Does sleep monitoring.
The software works on my iPhone but is not spectacular. To get heart rate you have to press the button - on the band or in the app - not continuous.
Rumour is that the new 3 version will be out on Wednesday or thereabouts. Given my experience I'd certainly wait to see what they announce before making any decision. Partner and I have just been discussing and she is also interested - and waiting.
Mi Band 3 now announced:
https://www.techradar.com/news/xiaomi-mi-band-3-news
Price looks good! Availability to the UK? - no idea.