Because there's a global pandemic in progress and it helps with contact tracing. Privacy concerns and public good are not mutually exclusive.

I think the point worth making is that a bad tracing app is a lot worse than no app at all. It’ll incorrectly give license to people that have been exposed to continue going going out. It’ll incorrectly isolate people who haven’t been exposed, it’ll destroy businesses based on false positives and it’ll destroy the credibility of effective lockdown measures.

Given what we know of the uk governments competence, I would want a strong study indicating its effectiveness before I go anywhere near this.