The Department for International Development (DfID) said last month the secretariat in London was "under performing" and needed "urgent reform".
Senior diplomatic and political sources - speaking to the BBC off the record - have accused the secretary-general, Lady Scotland, of "poor leadership".
But her spokesman said she had backing from all 52 Commonwealth countries that had elected her.
He added that the Labour peer had also launched a programme to modernise the Commonwealth Secretariat.
Tim Hitchens, a senior Foreign Office official and former ambassador to Japan, has been put in charge of a team preparing for the Commonwealth summit in London next year.
Mr Hitchens, a former assistant private secretary to the Queen, will be based in the Cabinet Office and will report directly to the prime minister.
Sir Simon Gass, a very senior official who retired from the Foreign Office last year, has been made acting chief operating officer at the Commonwealth Secretariat.
He was appointed at the suggestion of the Foreign Office which is funding his salary. He is working directly with Lady Scotland at the secretariat's headquarters at Marlborough House in London.
The appointments are being seen in Whitehall as an attempt by the government to shore up a troubled organisation at a crucial time.
Ministers are keen to ensure that a meeting of Commonwealth trade ministers in London in March is a success and shows how Britain after Brexit can do more trade with countries outside the European Union.
They also want to guarantee that the secretariat is capable of organising the heads of government summit next year that will be hosted by the Queen, who is head of the Commonwealth.
Senior ministers will meet next week to discuss the agenda for the summit for the first time.
Last week, Theresa May spoke of the "unique and proud global relationships" the UK has through the Commonwealth.
The secretariat helps run the group of 52 mostly former British colonies that make up the Commonwealth and that are home to some 2.3 billion people, more than a quarter of the world's population.
In a highly critical report in December, DfID threatened to withdraw its funding from the organisation unless it improved its performance.
"The Commonwealth Secretariat continues to under perform," the multilateral aid review concluded.
"Improvement is essential if DfID is to continue to fund the organisation's Commonwealth Fund for Technical Co-operation."
This is worth about Â£20m per year.
The report added that the secretariat needed particularly to focus on improving "transparency, results measurement, human resource management, risk management, financial management, and budget discipline".
The secretariat said the review related to the period before Lady Scotland took up the post of secretary-general last April.
Since then, the peer - who was attorney general in Gordon Brown's government - has faced much criticism.
She has been accused of financial extravagance over the refurbishment of her official residence and attacked for appointing political allies to key posts in the secretariat. She has always denied the accusations of wasteful spending and insisted no procurement rules were broken.
Her allies have also claimed the attacks were prompted by disaffected Commonwealth staff unhappy with the reforms she was introducing.
A spokesman for the secretariat said: "Secretary-general Patricia Scotland has the backing of the 52 Commonwealth member states who elected her.
"Since taking office on 1 April 2016, the Secretary-general has been focused on helping Commonwealth countries to achieve the United Nations Sustainable Development Goals, working towards the delivery of international climate change goals set out after Cop 21 in Paris and Cop 22 in Marrakesh, and to uphold The Commonwealth Charter."
"She has identified the following priorities: tackling the existential threat of climate change; promoting trade, good governance and human rights; ending violence against women and girls and promoting gender equality; and providing new opportunities for Commonwealth young people and enabling the next generation to achieve their full potential.
"Secretary-general Scotland has also launched a programme to modernise the Commonwealth Secretariat.
"When it comes to employee matters, we follow best international practice and never comment about individual staff. But it's only sensible that the Secretariat employs people of the highest calibre and those who have a track record of success in their respective fields."
But such are the concerns about Lady Scotland that some senior diplomats have even interpreted the fact that the Queen will not attend a major Commonwealth function in March as a signal of royal displeasure, something that is strongly denied.
The Queen will attend various events on Commonwealth Day, including a service at Westminster Abbey, but she will not attend the regular reception at Marlborough House, an event she rarely misses.
A Buckingham Palace spokesman told the BBC: "I can confirm that the Queen will be taking part in events during the course of Commonwealth Day, although on this occasion she will not attend the evening reception. Her Majesty will be represented at the reception by the Prince of Wales."
Well placed royal sources said this was a common sense and practical decision to ensure the Queen's programme was suitably paced on a busy day.
They also insisted it was wholly incorrect to link the decision to any debate about the Commonwealth Secretariat.
They noted that the Queen had regular contact with Lady Scotland and that there was a lot  of precedence for the Prince of Wales to represent the Queen on Commonwealth duties.
But that is not how it is being inferred by some in the Commonwealth.
One senior source said: "The Queen has only got to nip down the road from Buckingham Palace to Marlborough House in a Bentley. It's not that hard. And yet she has decided not to come.
"The Palace are thinking there is so much more to be done with the Commonwealth and yet they are lumbered with such poor leadership. The Commonwealth is stuffed.
"The High Commissioners have all given up on (Lady Scotland). They have other fish to fry. I do wonder if she can survive. She just treats people appallingly. And she has this political tin ear."
One parliamentary source said: "Baroness Scotland has got this wrong from the beginning. It is an inbuilt arrogance. She appoints mates, people who don't have the relevant experience.
"The way she handled the [official] house was all wrong. There is a lot of concern. I am not surprised the palace is getting a little edgy."
Another diplomatic source said: "What is happening is very sad. The morale at the secretariat is very low. [The Commonwealth] is the closest thing to Her Majesty's heart. If she doesn't come, it will be interpreted in this way.
"We in the Commonwealth preach transparency and accountability. We should practise it."
The government has drafted in senior officials to support the Commonwealth amid concerns over the way it is being run, the BBC has learned.