All 20 players and 11 management personnel in the Pakistan touring party have tested negative for coronavirus since arriving in Britain, the England and Wales Cricket Board (ECB) said on Tuesday.
The ECB added that England's latest round of tests, for their training group and management conducted on Monday had also yielded a complete set of negative results.
England players and staff have now had three Covid-19 tests.
The ECB's announcement followed a statement from Pakistan that six more players had been cleared to join the tour after recording two successive negative Covid-19 tests.
But the other four of the 10 players who originally tested positive for the virus last week will have to stay in Pakistan for now after failing further tests.
Mohammad Hafeez, Wahab Riaz, Mohammad Hasnain, Shadab Khan, Mohammad Rizwan and Fakhar Zaman are now eligible to travel to England and join the original squad that left on Sunday, the Pakistan Cricket Board said.
"All the six players were re-tested on Monday, following their first negative test on 26 June," the PCB confirmed.
However, Imran Khan, Kashif Bhatti, Haider Ali and Haris Rauf tested positive for a second time.
They will not be allowed to travel to England until they have recorded two consecutive negative tests.
Pakistan will play three Tests and three Twenty20 internationals against England starting in August, with the exact dates still to be confirmed.
The Pakistan squad arrived in England late Sunday and have started a 14-day mandatory quarantine period before intra-squad practice games.
A 30-strong England squad and support staff are currently in a bio-secure training camp at the Ageas Bowl ahead of next week's opening Test against the West Indies.
This first fixture in the three-match series will mark the return of major international cricket from lockdown.