For Keir Starmer’s Labour critics, his second king’s speech, in which the government set out what it would do in parliament over the next 12 to 18 months, was a crystallisation of everything that was wrong with the prime minister’s strategy.

Over 34 bills and three draft ones, Starmer set out a programme he said would “make this country stronger and fairer”. But the package, which included limiting trial by jury, reshaping the NHS and moving the country closer to the EU, fell short of what some in the prime minister’s party feel is needed to win back voters’ trust.

“Most of this is incrementalism,” said one Labour MP. “This sums up where we have gone wrong in the first two years in government. We talk about not going back to the status quo and then propose boosting growth by tweaking the wording of regulators’ remits.”

Harry Quilter-Pinner, the head of the Institute for Public Policy Research, called for “much bolder action on the cost of living, including rent controls, alongside longer-term reforms to growth, the state, and Britain’s relationship with Europe”.

Starmer’s legislative agenda is made up of measures that have previously been announced but for which the government has not yet found time. Some of them involve major changes to the way public services are run.

An NHS modernisation bill will legislate for the abolition of NHS England which the health secretary Wes Streeting has already announced. An education bill will enact the sweeping changes to special educational needs provision which the education secretary unveiled at a speech earlier this year. A courts bill will limit trial by jury in a bid to reverse some of the backlog gumming up the courts system.

Other bills, however, appear to do less than they promise, and display what critics say is Starmer’s characteristic reluctance to embrace trade-offs.

A regulating for growth bill promises to help Britain to “compete on the world stage”, something it will achieve largely by giving regulators a mandate to promote growth. When asked whether this would mean giving less priority to other factors such as safety or the environment, Downing Street said this would not have to be the case.

“It’s not about deregulation,” the prime minister’s spokesperson said. “It’s about giving greater weight to economic growth when making decisions, without weakening safety, environmental or consumer protections.”

The problem for the prime minister is that the king’s speech came against the backdrop of a major policy debate within the Labour party, prompted by the manoeuvrings of various potential leadership candidates.

In competing publications on Wednesday, two groups of Labour MPs set out their visions for what the party should be doing instead.

The Labour Growth Group, whose chair, Chris Curtis, is an ally of Wes Streeting and called this week for the prime minister to resign, wants a significant rise in capital gains tax to pay for a reduction in national insurance. The group also wants a major package of devolution that would allow mayors to tax and spend, as well as changes to the structure of government, including the creation of a new office of the prime minister.

Meanwhile the soft-left Tribune group, many of whose members want to see Andy Burnham replace the prime minister, want greater public ownership of utilities – particularly Thames Water. They are also calling for changes to the government’s fiscal rules to allow it to borrow more, but only after the next election. In the immediate term they want to levy a new land and property tax to replace stamp duty.

For some of Starmer’s critics, these proposals show the party is having the kind of in-depth policy conversation it should have had before the election. “We weren’t discussing ideas for how we were to run the country, and we didn’t develop a good enough or sufficient plan for government for when we got there,” Curtis told an event in Westminster on Tuesday evening.

Some of the prime minister’s allies say the ideas being promoted by competing factions within the party are not very different from what the government is doing anyway.

Starmer was planning to launch his own plan to create an “office for the prime minister” this week before he was derailed by having to defend his job against a possible leadership coup, sources say.

Even his critics argue the party should continue to be bound by the manifesto on which he was elected – limiting the scope for major changes, for example to the UK’s relationship with the EU or the amount the government can borrow. “We need to stick to our manifesto,” said Miatta Fahnbulleh, one of the ministers who resigned this week. “It’s more about how do we put the manifesto up in lights.”

Curtis is blunter in his assessment of the prime minister’s policy failings. “What we need to hear from the prime minister is what are the barriers he needs to remove so change can happen quicker, and so that we can get our economy back into the place where it’s growing and delivering for people,” he said on Tuesday evening.

“Because at this moment in time isn’t.”