Chilwell and Mount interacted with Chelsea team-mate Gilmour following full-time of England’s goalless draw with Scotland, with Gilmour having since tested positive for Covid-19.
The Three Lions are preparing for Tuesday’s crunch Group D clash with the Czech Republic.
But Gareth Southgate’s preparations have been rocked by news that Mount and Chilwell are having to isolate after coming into contact with Gilmour.
Watch: Major blow for Scotland as Billy Gilmour tests positive for coronavirus
A statement from the Football Association read: “As a precaution at this time and in consultation with Public Health England, Ben Chilwell and Mason Mount are isolating after interaction with Scotland player Billy Gilmour at Friday’s match.
“The pair will be kept away from the rest of the England players and wider support team, pending further discussions with PHE. The entire squad had lateral flow tests on Monday afternoon and all were again negative, as was the case with Sunday’s UEFA pre-match PCR tests.
“We will continue to follow all Covid-19 protocols and the UEFA testing regime, while remaining in close contact with PHE.”
Mount had been due to appear at the pre-match press conference alongside England boss Southgate.
Watch: Steve Clarke challenges Billy Gilmour replacement to make himself Scotland hero