The duo will train individually in private areas of England’s St George’s Park training base during their isolation which last up to and including Monday June 28.
A statement from the England camp read: “We will continue to follow all COVID-19 protocols and the UEFA testing regime, while remaining in close contact with PHE.
“The entire England squad and staff had lateral flow tests on Monday and all were again negative, as was the case with Sunday’s UEFA pre-match PCR tests.
“Further tests will be carried out as and when appropriate.”
No member of the Scotland set-up has been identified as a close contact of Gilmour.
England’s Mason Mount and Ben Chilwell to isolate following Billy Gilmour contact