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Travelers from the US to the UK are likely to be allowed in but quarantined, according to UK Travel: How Quarantine Will End For Some Europe Arrivals, Not US (mirror) published on 2020-06-25:
Travelers arriving from France, Italy, Spain, Germany and Greece are among those who will soon dodge UK quarantine. And vice versa.
But the United States, Portugal and Croatia are not set to make it onto the list of countries with whom Britain is setting up quarantine-free βair bridgesβ, according to British media reports.
Update 2020-07-03: info above confirmed by https://www.independent.co.uk/news/uk/home-news/uk-coronavirus-red-list-travel-us-ban-lockdown-quarantine-latest-a9599241.html and BBC news: