"Mr McGrath suggests testing and contact tracing everyone in the UK who is sexually active"

I don't. I say that isn't a practical suggestion, but that everybody who has a lifestyle in which they have sex with many people, including especially strangers, is crazy and irresponsible if they don't get checked regularly.   As the saying goes, when you sex with someone, you have sex with all the people they've had sex with, and all the people they've had sex with and... And of course that is likely to include a range of sexual identities.

But compulsory registers wouldn't be a realistic option, even if they were desirable.