As someone else pointed out Dr Fauci does not have any say, he just gives his medical opinion. I thought last month Trump said he would look to end the Europe travel ban 'soon', and as other have correctly pointed out that will come any day he feels like. September does however seem to make the most sense and be the most likely.

Of course he needs to remember Florida is a very important state for US elections, and it makes a lot of money from European tourists in the October holidays!

Regards a UK-US arrangement, I do not for one minute think the UK would insist on a 14 day quarantine for Americans if the US was prepared to drop their ban. The government knows how important the US is to the economy, that is why the US is on the 45 country list of priority countries to be exempted from quarantine. It includes the EU27, Switzerland, Norway, Iceland, several Caribbean islands, Australia, NZ, South Korea, Hong Kong and the USA/Canada.