Senior legal figures are warning Boris Johnson against interfering with the independence of the judiciary, amid mounting concern over the new government’s plans to overhaul Britain’s unwritten constitution.

Prominent figures in the Lords are also worried that the prime minister is planning to curtail their powers as part of a forthcoming review, with opposition parties already discussing how they can push back against any power grab by Downing Street.

Concerns have been raised in the legal profession by a pledge in the Queen’s speech last week for a new constitution, democracy and rights commission that will examine “how our democracy operates”. It follows September’s historic decision by the supreme court to rule Johnson’s suspension of parliament unlawful.

Simon Davis, president of the Law Society of England and Wales, warned those drawing up the scope of the new commission to safeguard the “delicate balance that underpins our unwritten constitution”.

“An independent legal profession and a government accountable to the people are fundamental elements of a nation rooted in the rule of law,” he said. “We must preserve and protect these principles at all costs. Our court system and our judges are there so the law laid down by parliament can be interpreted. In a mature democracy, it is crucial that the independence of this process is maintained.

“These pillars are intrinsic to the prosperity of the country and to its international standing. And while the precise content of the government’s plans remains unclear it is important for the Law Society to say from the outset that the independence of our judiciary must be safeguarded in this review.”

Peers and senior civil servants are concerned that the new government is planning to use constitutional reform to hold a sword of Damocles over the heads of potential critics. They fear it is designed to discourage them from holding up its Brexit proposals and domestic programme. Johnson’s team is also understood to be examining major changes to how Whitehall works, with some departments facing the prospect of being split up or abolished altogether.

Government insiders have suggested that the idea of a US-style appointed supreme court is not being considered. However, Johnson has previously warned that “some form of accountability” may be needed if judges interfere in political decisions, while the attorney general, Geoffrey Cox, has raised the idea of parliamentary scrutiny of judicial appointments.

Boris Johnson serves Christmas lunch to British troops stationed in Estonia. Photograph: Stefan Rousseau/PA

It is expected that the government’s review, of which more details will be given in the new year, will include a re-examination of the relationship between parliament and the government, following the trench warfare between the two while Johnson led a minority government. It is also expected to look at so-called “prerogative powers” – those powers that the government can use without parliament’s approval. Currently, their use can be challenged in the courts, which led to the ruling against Johnson’s prorogation of parliament.

Senior peers are already expecting the government to attempt to strengthen the supremacy of the Commons, as well as limit the amount of time the Lords can hold up legislation.

Dominic Cummings, the prime minister’s senior adviser, is understood to be frustrated by the length of time it takes legislation to reach the statute books. There is also concern inside Johnson’s team that it takes so long to get infrastructure projects off the ground that new Tory voters in small towns might not believe that the government is listening to them.

With Johnson’s 80-strong majority in the Commons, the Lords is likely to become one of the most important checks on his plans. Opposition parties in the Lords have already arranged a cross-party group, to meet after Christmas, to coordinate their response. The group will debate which fights they take on with the government.

“At the moment, the Tories’ tails are up,” said one senior figure involved. “Any amendments in the Lords will just be overturned. It won’t be hand-to-hand combat early on and we will have to find our way, but the Lords isn’t quite as pro-Boris as the Commons is now. We’ve already started drawing up amendments and we are worried that a power grab is coming up.”

Significant Whitehall changes are on the cards, with Cummings keen to tackle what he regards as long-running and crippling failings within the civil service. There is speculation about a new immigration department, the abolition of the justice and international development departments, and the arrival of more outside expertise into government. The imminent abolition of the Department for Exiting the European Union has already been announced. A cabinet cull is also on the cards in February, though no decisions have been taken. Jacob Rees-Mogg, the Commons leader, is seen as vulnerable.

Cummings is keen to apply to Whitehall some of the principles pioneered by George Mueller, a missiles engineer credited with making Nasa an organisation capable of a successful expedition to the moon. “Saving time saves money,” Cummings once wrote on his blog. “Mueller focused on speed and saving time. Whitehall now works on opposite principles: its default mode is to go slower and those who advocate speed are denounced as reckless. Repeatedly in the [Department of Education, where he worked as an adviser under Michael Gove] I was told it was ‘impossible’ to do things in the period I demanded – often less than half what senior officials wanted – yet we often achieved this and there was practically no example of failure that came because my time demands were inherently unreasonable.”