The board has said it will announce results of all tests on Saturday (June 27).
Khan reiterated that the six players who have now tested negative will undergo a third round of testing at some stage next week and if they return negative, then the PCB will make arrangements to send them to England.
PCB CEO Wasim Khan said: "With the Test series being played first in August, [head coach] Misbah [ul-Haq] is satisfied with the group of players that are traveling on Sunday as the focus will be on red-ball preparation. Therefore, once they are retested and receive a second negative result under the PCB testing programme, they will be available to join the squad in England".
The board chief executive Wasim Khan said the players can rejoin the squad of 18 players if they later test negative.
"Following advice from leading sports science experts and as per the United Kingdom government regulations, players who have tested positive during the PCB testing process will be unable to travel on Sunday", the press release stated.
"The private test they [Mohammad Hafeez and Wahab Riaz] made a decision to have carried out was outside the PCB testing process".
The Pakistan Cricket Board expressed concern on Friday over the positive results from 10 of the 29 cricketers chosen for the tour.
They have been advised by the PCB medical panel to observe "strict quarantine", with the board providing them complete support. Of those missing the start, only wicketkeeper Rizwan would be classed a first-choice Test player. Pakistan fast bowler Musa Khan and under-19 captain Rohail Nazir were among five reserve players and both tested negative.
According to PCB, Pakistan bowling coach Waqar Younis will join the side directly from Australia, while veteran all-rounder Shoaib Malik "is expected to travel around July 24".
Pakistan will now quarantine and train at Worcestershire's Blackfinch New Road for 14 days, before a planned move to Derbyshire's Incora County Ground on July 13 to begin internal warm-up matches.
Squad flying off on Sunday includes Azhar Ali (Test captain), Babar Azam (T20 captain), Abid Ali, Imam-ul-Haq, Shan Masood, Asad Shafiq, Fawad Alam, Iftikhar Ahmad, Khushdil Shah, Sarfaraz Ahmed, Faheem Ashraf, Mohammad Abbas, Naseem Shah, Shaheen Afridi, Sohail Khan, Usman Shinwari, Imad Wasim, and Yasir Shah.
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