The Lady Chief Justice stressed decisions on deploying judges were “exclusively a matter for the judiciary” amid attempts by ministers to quell concerns from rebel Tory MPs over the Rwanda Bill.

The most senior judge in England and Wales made the comments after plans were announced to draft in more judges and free up courtrooms in a bid to speed up migrant appeals.

Downing Street said the move showed the Government was “taking every conceivable step” to get Rwanda deportation flights off the ground.

It is understood 150 judges could be brought in to deal with cases. But a former justice secretary warned hiring judges could be a “challenge”.

Asked about the practical implications of the move, the Lady Chief Justice – the first woman in history to hold the position – said headlines about the plan drew “matters of judicial responsibility into the political arena”.

In her first appearance before the Commons Justice Committee since her appointment, Lady Carr told MPs on Tuesday afternoon: “Parliament has legislated, we – the judiciary – have acted in preparation for that legislation.

“But to be absolutely clear, matters of deployment of judges, the allocation of work for judges and the use of courtrooms is exclusively a matter for the judiciary, and more specifically, a matter for myself and the senior president of the tribunals. And it’s really important that people understand that clear division.”

Committee chairman Sir Bob Neill said there was a long-standing “constitutional convention” that meant members of the judiciary were not asked to “come into the realms of politics” or be asked to comment on “matter of potential political controversy or emerging government policy” but said this question invoked an “exception to the convention” as it related to the ”operational impact of any potential actions upon the courts”.

Justice Secretary Alex Chalk said he had asked more judges to be appointed to the First-tier and Upper Tribunal to speed up migrant appeals.

He told the Commons recruitment would “conclude in the next few months and new judges will be appointed, trained, and start sitting from this summer”.

In the meantime, the judiciary had identified judges who could provide 5,000 additional sitting days while extra space had been prepared, making a total of 25 courtrooms available for hearings.

In a written ministerial statement to Parliament, he said: “We are confident that, with the additional courtroom and judicial capacity detailed above, in line with projected levels agreed with the Home Office, the vast majority of Illegal Migration Act appeal work will be dealt with by the courts in an expedited manner.”

But he stressed the “decision on whether to deploy additional judges temporarily to the Upper Tribunal, including when they sit and the courtrooms they use, is for the independent judiciary and will be taken by the relevant leadership judges at the time and in the interests of justice.”

Downing Street later said Rishi Sunak still aims to have flights running to Rwanda by the spring, despite the announcement stating extra judges would not in place until the summer.

The Prime Minister’s official spokesman said while the Bill would ensure the bar for legal challenges is “set extremely high”, it is “also right to ensure that we have the resources to deal with the minority of claims should they arise”.

When it was put to him that some rebels argued the move was an acknowledgement that the Bill would not put a stop to legal challenges, the Number 10 official replied: “No, I think it demonstrates that we are taking every conceivable step to ensure that we can get flights off the ground as quickly as possible.

“The spurious challenges we have seen before will be blocked through the Bill, the systemic challenges will be blocked.

“We have heard from leading judges, leading lawyers, who say the Bill will do the job that it needs to do, whether that is blocking challenges on modern slavery, on asylum — those sorts of spurious challenges will not be allowed.

“But it is right, in the small minority of cases, that we have resources put in place if needed.”

But former Tory justice secretary Sir Robert Buckland told the Commons ministers will face “quite a task” in recruiting more judges to deal with the anticipated swathe of new legal claims should the Rwanda plan go ahead, adding: “It is going to be quite a challenge” and will need a “particular way in dealing with cases that will have to be much quicker than the status quo”.

He also asked: “If we can do it in immigration, can’t we do it in crime as well, please? I think it is a high and timely reminder of the fact that our justice system is pretty important and that despite my best efforts to increase funding, which we did do, more needs to be done in order to ensure that those backlogs are dealt with.”

Law Society of England and Wales president Nick Emmerson said the proposals “once again illustrate the apparent incoherence at the heart of the UK government’s immigration policy”, adding that they “do not overcome the fundamental flaws” of the Bill and instead try to “deal with some legal challenges more quickly with more judges at a time when the entire justice system is suffering from a lack of judicial capacity”.