Boris Johnson is still prime minister, for now, and has appointed a cabinet, so technically the business of government should be able to continue. With the nation gripped by a cost of living crisis, and action needed on everything from education to energy, the ministerial in-trays are overflowing. But the chances of a “lame-duck” administration getting much done look decidedly thin. Here are some of the major policies that could stall amid the chaos.

Energy

It promised to be a momentous – and feisty – week in the energy industry as long-running battles came to a head. A decision on approval for the £165m plans for Britain’s first new coalmine for decades, near Whitehaven in west Cumbria, had been expected but was delayed. A review into fracking, originally expected last week, is yet to emerge. A decision on planning approval for the Sizewell C nuclear reactor in Suffolk, opposed by environmental campaigners, was due on Friday. It has now been pushed back to 20 July.

Gambling clampdown

A once-in-a-generation reform of the UK’s out-of-date gambling laws was due to be unveiled next week, but that has been thrown into doubt by the resignation of gambling minister Chris Philp. The white paper is expected to include tougher stake limits on online casino games and affordability checks to ensure punters don’t lose too much, unless the proposals are watered down. Other policies hanging in the balance include the creation of a gambling ombudsman, a mandatory levy on operators to fund addiction services and a possible ban on betting logos on football shirts.

Northern Ireland protocol

Johnson, like his predecessor, may leave office with the issue of trade with Northern Ireland unresolved. His government is pushing through legislation to rip up arrangements he signed into law that impose checks on goods going from Great Britain to NI.

On Thursday, EU leaders quickly called for Johnson’s successor to abandon the plans to deliberately break international law, which could cause a broader trade war between the UK and its biggest trading partner. Warmer relations could also open the door for the UK rejoining the EU’s €90bn (£76bn) Horizon science research scheme.

HS2 in the north

The high-speed rail network has always been opposed by a majority of Conservative voters and particularly among the Brexit wing. Johnson likes big infrastructure projects and backed it. Nonetheless, in his leadership campaign, he whipped up votes by promising to review it – even if, once elected, he handed that review to a former chairman of HS2.

Too much work has surely been done on the first leg from London to Birmingham to go back now without colossal waste, and phase 2a to Crewe has passed through parliament. But a new leader could still choose to scrap the rest.

Education

Teachers’ pay is the top item for the new education secretary, James Cleverly – he needs to publish the recommendations of the School Teachers’ Review Body before the end of term or risk further angering teachers in England before strike ballots in autumn.

Exam results for A-levels and GCSEs arrive in mid-August – and will see steep falls in top grades compared with last year. Whoever is education secretary will have to clearly communicate to unhappy students and parents why that has happened. The associated university admissions round could be a similar nightmare for ministers.

The schools bill going through parliament is in trouble and needs major retooling to overcome opponents in the Lords who see it as a centralising power-grab over academies by government.

The higher education freedom of speech bill is also facing opposition in the Lords, and has now lost its major sponsor in Michelle Donelan as minister. It may be further delayed as its flaws are exposed.

Other policies left dangling include the consultation on the review of special education needs and disabilities that closes soon and needs urgent focus if reforms are to make progress, while new policies on post-Covid catch-up and school attendance also demand attention from ministers.

Retail taxes

The rapid change to the retail industry brought by the internet has not been matched by updates to how it is taxed. The government has consulted on reforming the system of business rates for shops and on an online sales tax for web retailers. A decision on the latter was expected by the autumn, but is already facing stiff opposition from Conservative-friendly thinktanks.

Online harms

Parliament is meant to be scrutinising the government’s online safety bill next week. A major change in the regulation of the internet, it would potentially require social media platforms, video streaming services and search engines to reduce the influence of foreign state-backed disinformation. Two champions of the bill, Nadine Dorries and Priti Patel, are still in office, and the government has said it will complete the next stage before parliament goes into recess on 21 July.

Human rights

Dominic Raab has had the Human Rights Act, brought in by Labour, in his sights for a long time. He wants a replacement “bill of rights” to allow the UK’s supreme court to ignore rulings by the European court of human rights (the arbiter of the non-EU European convention on human rights).

Tacked on to the bill is a proposal to prevent the wealthy from using the threat of expensive court action to silence journalists or campaigners, by bringing so-called strategic lawsuits against public participation, or Slapps. A consultation has closed, but detailed proposals have not been published.

Immigration

The government’s decision to ship refugees from the UK to Rwanda drew opposition ranging from Tory backbenchers to the Archbishop of Canterbury. It has also failed so far to get through the courts, after a first planned flight was prevented from leaving. The scheme’s architects, Johnson and home secretary Priti Patel, are both still in office, and the government’s lawyers are due to argue their case for the flights to go ahead on 19 July. Even if it passes that hurdle, a future administration could easily ditch the policy.