Three players and four members of the management team tested positive after taking PCR tests.
In a statement, the England and Wales Cricket Board said: "In collaboration with Public Health England, Public Health Wales and Bristol Local Health Authority, those impacted will now observe a period of self-isolation from July 04 following the UK government's protocol on quarantine.
"The remaining members of the party have been deemed close contacts and will also isolate.
"The ECB have confirmed the Royal London ODIs and the Vitality IT20s against Pakistan will go ahead. Ben Stokes will return to England duties and captain the squad - which will be named in the next few hours."
The isolation period will span all three ODIs against Pakistan, which start on Thursday in Cardiff.
Ben Stokes is to return to the England side as captain after several weeks out with a fractured finger, while the rest of the new team to face Pakistan will be named later on Tuesday, Sky News reports.
Meanwhile, the Sri Lankan team arrived in Sri Lanka today (06) after their disastrous tour of England.
(Excerpts from Sky News)