Daily worship is compulsory in all British state schools - it has to be broadly Christian. (Not sure about private but I suspect many follow suit).
In primary schools this tends to be a hymn / song and a short prayer. Secondary don't tend to do hymns and prayers but will often have assemblies focused on community and charity.
All primary schools will tend to do various religious celebrations but almost definitely Christmas activities, Easter and harvest festival.
This is seperate to RE which is part of the curriculum and which teaches about different religions and beliefs (including humanism and atheism).
You can withdraw your child from collective worship and / or RE (although not sure why you would want to withdraw from RE as it is not instruction but knowledge).
However, I would caution against it as it may make your child feel left out.
If it's any consolation - my youngest DD is staunchly atheist (even more so than me and DH) - when we moved she had the choice between a small church school with a prayer corner and the bigger primary in the town. She chose the church school, always joined in the singing, nativity, carol concerts etc (her choice) and it did absolutely nothing to sway her beliefs - if anything it made her even more atheist!
The UK is not an overtly religious nation despite being a formally Christian nation (much less religious than the supposedly secular USA) and most of us being brought up singing hymns hasn't changed that.
Having a good hymn sing along has actually turned into a bit of a culture night out for adults (Google Primary School Bangers by Jason Partridge and look up the Jason Manford segment relating to it) - but certainly not for worship 🤣