Will my local authority alert system still work one my line once it has been migrated over to digital voice. I only have a telephone line but NOT broadband.
As you do not have broadband, nothing is going to happen right away.
See https://www.draytek.co.uk/information/blog/the-end-of-analogue-phone-lines-pt1
You will find page 2 of the article useful.
https://www.draytek.co.uk/information/blog/the-end-of-analogue-phone-lines-pt2