Tory chief whip John Lamont said it was timed to "cause the most upset".
He resigned from his post as chief whip in October following a media backlash.
But Mr Cameron admitted he had had a word with Chief Whip Sir George Young.
Mr Howells is replaced as minister for lifelong learning by George Mudie, formerly deputy chief whip.
The bottom line is that this is not a matter for the chief whip.
We are in Act Two of the Whitehall farce "What The Chief Whip Said".
She met Chief Whip Sir George Young and she remains suspended from the Conservative parliamentary party.
Baroness Anelay of St Johns, government chief whip, assured Lord Foulkes that room would be avoided.
He is also deputy government chief whip and Lib Dem chief whip in the House of Lords.
The chair of the local party is expected to inform the Chief Whip of the decision later.
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Nonetheless, Nick Brown, Labour's chief whip, has decided to inquire into the claims made by Mr McMaster.
They were (including the chief whip, carted in from hospital where he was awaiting a heart operation).
Some Labour politicians, most notably Donald Dewar, the party's chief whip, are still arguing for this approach.
All of which leaves the Chief Whip in his job but still in a very bad place indeed.
Sir Stuart is understood to have met Labour chief whip Rosie Winterton on Wednesday afternoon to discuss the claims.
Plaid AM Jocelyn Davies, her party's chief whip, said Miss Jenkins had informed her she would be in London.
Cyril invited me to work in his office when he was Chief Whip.
Mr Mitchell resigned as chief whip over claims he swore at police officers during a confrontation in Downing St.
Rosie Winterton is the only name entered for the ballot for chief whip.
Andrew Mitchell quit as chief whip after it was alleged he called police "plebs" - a claim he denies.
But when it emerged that the Labour chief whip had warned her a year ago, she had to go.
Suddenly the parliamentary arithmetic gets interesting and the new chief whip, Sir George Young, could face an early challenge.
His bullish character saw him promoted to be his party's chief whip in 1975 under the then leader Jeremy Thorpe.
The Labour peer accused government Chief Whip Baroness Anelay of St Johns of a "sadistic desire to keep us going".
He quit as Tory chief whip after it was alleged he called Downing Street police officers "plebs", which he denies.
By this stage Mr Brown, appointed chief whip by Tony Blair, was a senior member of the new Labour government.
The Chief Whip Janice Gregory has summarily removed three Labour members, including its chair Christine Chapman, from the committee at extremely short notice.
The MP for Mid-Bedfordshire said she had been given permission to take a holiday by the then Chief Whip Andrew Mitchell.
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"Neither the prime minister nor the chief whip have proved capable of coming clean swiftly and putting this right, " said Ms Cooper.
Government Chief Whip Andrew Mitchell authorised the payment in his last day in his previous job of international development secretary in September.
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