But Philip Hammond, Boris Johnson, Amber Rudd and David Davis are among key figures expected to stay in place.
Damian Green was the third minister to leave the cabinet in the space of a few weeks, after the defence secretary and worldwide development minister both quit - all three following separate scandals.
But it began in a farcical fashion when her Conservative party announced a new chairman on Twitter, only to delete the tweet and later name another lawmaker for the post.
But the reorganization quickly became more remarkable for what May didn't do rather than what she did, highlighting the difficulties imposed by Brexit and the erosion of the prime minister's authority since the ill-judged vote in June that cost her party its parliamentary majority.
Lewis had until today been the Minister of State for Immigration and was the first minister to have been summoned to No.10 to meet with the Prime Minister this morning.
Stephen Kinnock, another Labour MP on the committee, said: "His passive-aggressive tone of the letter demonstrates that the government doesn't have a clue".
However, Mrs May said: "As Prime Minister, my job isn't just about what I think about something, it's actually about looking at what the view of the country is".
Plane Left Teetering On Cliff In Turkey
According to The Associated Press , no one was hurt in the incident, and everyone on board was evacuated safely. Pegasus said in a statement the aircraft had been successfully evacuated and no injuries were reported.
May said her reshuffle helped the government look "more like the country it serves". Newspapers said he refused to accept a new post, although a source close to May denied that, and said Hunt simply persuaded her.
Reports suggests more junior ministerial appointments would continue into a second day on Tuesday.
Whoever will be chosen to replace Green will be a significant signing as he was effectively an acting deputy Prime Minister, standing in for May when she was unable to attend certain events such as PMQs.
May's room for manoeuvre is limited by heading a minority government and the need to maintain a delicate Cabinet balance of eurosceptic and pro-European ministers as major Brexit decisions loom.
Negotiations on a transition deal begin this month, while the toughest talks, on Britain's future relationship with the European Union including trade, are set to start in March.
Meanwhile, the Northern Ireland Secretary James Brokenshire has resigned on health grounds. But the former justice secretary has not been given the title of first secretary of state, which marked Green out as Theresa May's effective deputy.
Environment Secretary Michael Gove, International Development Secretary Penny Mordaunt and International Trade Secretary Liam Fox all remain in the same jobs.
Sir Patrick McLoughlin, the outgoing Conservative party chairman, has confirmed that he has left the cabinet.