To be clear, a strategy of allowing this to spread unchecked will result in 10s of millions of people dying around the world.
Current advice is to self-isolate for 7 days if persistent cough suddenly appears and/OR a temperature of 37.5°C (that is not high temperature).
That sound like good advice, but they are not going to test those cases unless it ends in hospital. And they don't want you to call to the NHS help line or go to the doctor (again, not bad advice but I see some people getting anxious about this; IMHO at least the help line should be available because most people aren't doctors).
Considering that it could be a mild case of the disease or any other common seasonal disease (I have two toddlers at home: they get ill), how can we tell we had passed the disease and we have some immunity?
Besides, if testing and tracing stops, it means there won't be information about the progression of the epidemic in the UK; which sounds to me like a bad idea (but I'm not an expert).
Considering how the Conservative government has been underfunding the public health system for 10 yeas, I understand how their approach can be seen by some as untrustworthy.
EDIT: I see this may be off-topic re: herd immunity, sorry about that.
Yes, there will. It will be inferred from hospital stats.
Testing and tracing (apparently; I'm no expert, parroting what I've read from experts) is only useful in the contain phase. After that, you're better focusing on slowing the spread in the delay phase.
That said, Singapore and China have shown success with testing, tracing, and extreme measures. The assumption of the UK Government, however, is that in the long-term these measures will fail and kill more people than following a delay phase strategy.