I understand Public Health England contact about 1 in 5 to check they are self-isolating, but as more countries are added to the list I expect they are overwhelmed to check even 10%.
Some newspapers a running a story about an air bridge between London and New York, just for residents of the two cities, being discussed by senior officials on both sides. NY has a rate of about 7.2 and London 11.3. The Americans are pressing for testing at the UK end, which is what people have been saying for months. Grant Shapps however doesn't have much faith in testing, so perhaps Bungling Johnson needs to intervene for this idea to get anywhere.