I'm not sure how they can improve it, as it requires public consent.
Here's a naughty story:
My sister's school (she's a teacher) was rife with the dreaded plague before Xmas. She visited my mum and dad and nan (the latter had received her 1st dose by then but still). My sis was paranoid so wore a mask, visor and kept her distance.
The next day, due to her paranoia, she went to get an LFT. No symptoms at all. Well, it was positive.
She told all our family and my mum implored her not to name them as contacts as she had already endured 2 isolations (much more exposed) and didn't want to over Xmas as they wanted to drop and run presents to us on a doorstep visit on Xmas day (we were also isolating ho ho ho). My sis didnt name anyone.
So, as you can see, how can the gov improve that?
Money, I guess some would say but can you imagine the fraud potential?
'hey mate, I hear your covid +, what a bummer, anyway, I fancy £500 so how about say we shared a car yesterday? Tell t&t. Cheers bruv"
What can the gov actually do?!