When the PCB agreed to the tour, they had announced a strict testing policy which meant that only players who twice tested negative for coronavirus would board the plane to England.
Those players did not board the plane on Sunday, though, as having tested positive initially they must now receive two negative tests in order to travel - their third tests will take place some time next week.
Three test matches and three T20 internationals are scheduled behind closed doors.
They will be sent to England as and when they return two negative Covid-19 tests.
A source close to Hafeez defended his action, insisting that the player was "very disturbed" after his first test came positive and he was obviously concerned for his immediate family.
"The private test they [Mohammad Hafeez and Wahab Riaz] chose to have carried out was outside the PCB testing process".
"The England & Wales Cricket Board can confirm that the Pakistan men's cricket team will arrive in the United Kingdom on Sunday 28 June to start preparation for this summer's tour of England, which includes three Test matches and three Vitality IT20s".
'With the Test series being played first in August, [head coach] Misbah [ul-Haq] is satisfied with the group of players that are travelling on Sunday as the focus will be on red-ball preparation.
After their arrival to Manchester, the squad will be transported to Worcestershire where they will undergo testing.
Players Shadab Khan, Haris Rauf, Haider Ali, Fakhar Zaman, Mohammad Rizwan, Wahab Riaz, Imran Khan, Mohammad Hafeez, Mohammad Hasnain and Kashif Bhatti first tested positive earlier this week.
As per the PCB testing programme, players who have tested positive have to show two negative tests before entering England in adherence to the United Kingdom government regulations.
The PCB originally had picked a 29-member playing squad for the England tour. Pakistan fast bowler Musa Khan and under-19 captain Rohail Nazir were among five reserve players and both tested negative. During the isolation period, the team will be allowed to train and practice.
First batch of players leaving for England: Azhar Ali (captain), Babar Azam (vice-captain), Abid Ali, Asad Shafiq, Faheem Ashraf, Fawad Alam, Iftikhar Ahmad, Imad Wasim, Imam-ul-Haq, Khushdil Shah, Mohammad Abbas, Musa Khan, Naseem Shah, Rohail Nazir, Sarfaraz Ahmed, Shaheen Shah Afridi, Shan Masood, Sohail Khan, Usman Shinwari and Yasir Shah.