Boris Johnson has kicked off a wide-ranging reshuffle of his top team by sacking three cabinet ministers, including removing Gavin Williamson as education secretary.

The education secretary confirmed his departure in a tweet, saying: “It has been a privilege to serve as education secretary since 2019.” He did not specify whether he had been given another post, saying only: “I look forward to continuing to support the prime minister and the government.”

The justice secretary, Robert Buckland, and housing and communities secretary, Robert Jenrick, also announced they had been removed, after meeting the prime minister in his House of Commons office on Wednesday.

Williamson had been widely tipped for the chop after a string of gaffes. The future of the foreign secretary, Dominic Raab, remains unclear, with many at Westminster expecting the former lawyer to be moved to justice in Buckland’s place.

The home secretary, Priti Patel, also widely tipped for a move, was not seen entering Johnson’s office, where bad news is traditionally delivered. Conservative party co-chair Amanda Milling was seen leaving Johnson’s office, however.

The prime minister’s official spokesperson had earlier said Johnson’s reshuffle would “put in place a strong and united team to build back better from the pandemic”.

The prime minister is also expected to undertake a significant reshuffle of his junior ranks, which could run into Thursday.

Johnson’s spokesperson said the reshuffle was the second part of the plan to relaunch government strategy following the winter plan for Covid announced on Tuesday. “Yesterday the PM set out his plan for managing Covid during the autumn and winter,” the source said.

“But the government must also redouble our efforts to deliver on the people’s priorities. The PM will be appointing ministers this afternoon with a focus on uniting and levelling up the whole country.”

Patel and Raab have been the target of public criticism, for the handling of migrant boats by the Home Office and of the Afghanistan withdrawal by the Foreign Office, respectively.

However, the pair have been longtime loyal allies and are likely to resist a significant demotion.

Others who could be in line to move are the environment secretary, George Eustice, and the Welsh secretary, Simon Hart.

Johnson is known to be keen to have more geographic diversity in his cabinet, which is predominantly from constituencies in the south or Midlands.

He has previously pledged to have at least one woman in the four “great offices of state” which would mean at least one woman is likely to be promoted should Patel be moved. The most likely candidate is Liz Truss, a favourite of Tory members, who could replace Raab.

The reshuffle will leave new ministers with only a few weeks to prepare for the Conservative party conference – and, most pressingly, for the government’s spending review, where departments have to make detailed submissions to the Treasury.

Asked whether the prime minister had discussed the job changes with his wife, Carrie Johnson, his spokesperson said no. Johnson’s former chief adviser Dominic Cummings tweeted on Wednesday morning that it would be a “Carrie reshuffle”.