When can we in the UK expect the one ui 3 beta program to start for us ?
Nothing definitive yet but imagine will be by end of year, though S20 devices will be first in line. see this thread https://eu.community.samsung.com/t5/galaxy-s20-s20-s20-ultra/android-11-does-anyone-know-when-it-wil...
Once a person has registered to become a beta tester with Samsung and accepted to become a beta tester via the Samsung Members app Samsung then supply the relevant information.
I wouldn't recommend to download beta software on your daily driver as beta updates can create issues with either your networks features and break things or things don't work properly as Samsung fine tune the beta software in updates as the programme progresses.
Current Phone ~
Samsung Note 20 Ultra 5G SM-N9860_256Gb SnapDragon 865+
Samsung One Ui 3.1/ Android 11.