Lady Justice Hallett’s handling of the London bombing inquests has done her chances of becoming the next lord chief justice no harm at all.

There isn’t a vacancy, of course, and Lord Judge, who celebrates his 70th birthday next week, is on excellent form.

But when the time comes for him to hang up his wig, Dame Heather Hallett, 61, could become the first woman to head the judiciary of England and Wales.

I hope this would mollify critics who complained last week when two vacancies in the Supreme Court were filled by men.

Indeed, no woman was even shortlisted. In my view, though, the court’s dearth of Chancery specialists is much more of a problem.

The other main contender for the job of lord chief justice is Lord Justice Hughes, 62, who is already vice-president of Court of Appeal’s criminal division.

That makes him number two to the lord chief justice on the criminal side. And Hughes is regarded as a stronger lawyer than Hallett.

But he does not have the experience of dealing with the wider world that is now a prerequisite for this most political of judicial posts.

Hughes may be better suited to the role of president of the Queen’s Bench division, a job which I understand will become vacant rather sooner.

Hallett has a background in criminal law, traditionally a requirement for appointment as lord chief justice.

So does Lord Justice Leveson, 61, who currently chairs the Sentencing Council and was previously senior presiding judge, a job with heavy pastoral and administrative burdens.

But to get to the very top of the judiciary it often helps to have a high-profile public inquiry under your belt.

You need to show that you can cope with the practical problems of running a court-like structure.

You have to be able to handle the lawyers, the parties and the media. And you have to come in on time and within budget.

As Hallett said at the end of the 7/7 inquests last Friday, she had completed the inquests into 52 deaths significantly under budget, despite setting her team extremely tight time limits.

‘We have managed to adhere to our timetable, to the very day and the very hour set,’ she noted, not without some pride.

By contrast, Lord Saville’s report on Bloody Sunday was not published until five years after the completion date he had set for himself.

As coroner, Hallett came over as tough and decisive.

She did not shirk from criticising the Security Service for showing surveillance photographs to a source that had been reproduced in such a way as to make the subject unrecognisable.

She expressed concern that parliament’s Intelligence and Security Committee had been ‘inadvertently misled’ by MI5.

She uncovered some disturbing failures by the emergency services and made what appear to be sensible recommendations, many of which one would hope are already in place.

Hallett may not have satisfied the families of those who died; perhaps nobody could. But she showed great sensitivity in ordering the names of all 52 victims to be read out at the closing session while confining the painful details of how each died to written public records.

Unlike Saville, Hallett was not overturned on by her colleagues in the Court of Appeal.

And she managed some deft footwork.

Under rule 43 of the Coroners Rules 1984, as amended in 2008, the coroner may make recommendations to those who may be able to prevent other deaths in the future.

These recommendations are contained in a report to the lord chancellor who may publish it if he sees fit.

It would clearly have been unsatisfactory for Hallett’s report under rule 43 to have been published some time after the inquest had ended.

She therefore obtained the lord chancellor’s permission to publish it herself at the same time as her findings.

Even more shrewdly, Hallett used her report to get round the requirement in rule 42 that a coroner’s verdict may not attribute criminal liability to a named person.

She was therefore able to name the four bombers as murderers of the 52 victims.

Until rule 43 was amended in 2008, the coroner had to confine her recommendations to those that might prevent deaths similar to those under investigation.

The need for similarity has been removed and recommendations may now be made relating to any risk of further deaths.

As a result, she has published a substantial report of 65 pages – much longer than one would expect.

But the bigger an inquest becomes – with teams of counsel taking over the coroner’s inquisitorial role – the more risk there is that it will be caught by provisions requiring a jury to sit.

This is needed if the death ‘occurred in circumstances the... possible recurrence of which is prejudicial to the health or safety of the public’.

Hallett was right to have decided that no jury was needed.

It would have delayed the proceedings, added complications when matters of national security were under consideration and made no difference to the final result.

She was also right not to resume the inquests into the four suicide bombers, adjourned pending related criminal proceedings.

All this suggests a determination to make the law work effectively in the public interest, even though the coronial system was never designed to deal with mass fatalities following a terrorist attack.

Hallett has already demonstrated her skills in chairing the Bar Council (in 2000) and Inner Temple, where she is Treasurer this year.

Surely it can’t be much harder to run the Court of Appeal?