Ministers could be forgiven for thinking that Lord Judge, the lord chief justice of England and Wales, had gone too far last week, overstepping the invisible line that separates the judicial from the injudicious.

There he was, introducing his annual report on criminal appeals and complaining about the "continuing burden of comprehending and applying impenetrable legislation, primarily but not exclusively in relation to sentencing".

And there he was again, giving evidence to the Lords constitution committee about the "extraordinary" effect of the government's public bodies bill, which gives ministers so-called Henry VIII powers to modify, merge or abolish a huge range of quangos. His concern that an "astonishing" number of acts now allowed ministers to repeal primary legislation will come as no surprise to the lord chancellor: Judge said as much to Ken Clarke at the judges' dinner in the summer.

But what really worries Judge is the threat posed by the public bodies bill to the independence of the judiciary. As he told the committee, schedule 7 would permit ministers to abolish bodies such as the Judicial Appointments Commission, the Criminal Cases Review Commission, the Sentencing Council and the Parole Board. These institutions had been created as independent public bodies and Judge argued that they should remain independent of the government of the day.

"I have made my views entirely clear, in the way in which it is appropriate for the chief justice to make his views entirely clear," he told peers. "And I very much hope that, as a result of a whole lot of people making their views entirely clear, very careful reconsideration will be given to the whole series of bodies in schedule 7 which currently perform a quasi-judicial function."

But when is it appropriate for a chief justice to make his views clear about pending legislation? That was the question put to him by Lord Goldsmith QC, the former attorney general.

"We have to be very careful not to be seen to be entering the political arena," Judge replied. Where there was a division along party lines, the judges had to be "extremely careful and tactful".

If the government had published a consultation paper, he continued, there was no reason why the judges should not respond. If no such paper had been issued, Judge thought it acceptable to warn the government's law officers about the practical consequences of a proposal. But that was as far as the judiciary could go in criticising bills. It was a delicate line they had to tread.

If anything, the judges are less willing to take on the government than they used to be. You don't have to go even as far back as 15 years to find the law lords voting against Michael Howard's police bill in parliament at the same time as they were hearing an appeal by the home secretary against restrictions on his power to set sentencing tariffs.

To Judge's evident regret, the last government passed legislation preventing serving judges – including the chief justice – from speaking or voting in parliamentary debates. At the same time, though, Labour gave senior judges much greater political powers.

Under an agreement known as the concordat, the chief justice is meant to sign off the annual budget for running the courts. Judge told the constitution committee last week that negotiations with the lord chancellor had not yet produced a deal for 2011-12. If no agreement was reached, the two sides might agree to differ and do the best they could. But Judge gave a public warning that he would bring the concordat to an end if the government offered a derisory sum. That, he said, would be a "disaster and a crisis of great magnitude".

If the chief justice is a thorn in the government's side, then it is a thorn of parliament's making. Senior judges did not ask to take on some of the powers of the lord chancellor but nor are they shirking the responsibilities they were given by the Constitutional Reform Act 2005.

Judge's guidance this week permitting Twitter to be used in court – provided tweeters ask first and there is no interference with the administration of justice – showed yet again his sensitivity to issues of public concern, in this case the needs of the reporters covering fast-moving stories.

I can no longer resist saying it. Far from stepping over the line, Judge's interventions are – generally – well-judged.

Joshua Rozenberg is a freelance legal writer, commentator and broadcaster