Devolution of power. Burnham has promised the biggest-ever "rebalancing of power" away from Whitehall, with English regions handed more control in areas including housing and transport by a new No 10 unit based in Manchester. The unit would be tasked with promoting "equivalent living conditions" across Britain, borrowing from an idea in the German constitution. He has also promised new opportunities to extend existing devolution settlements in Scotland, Wales and Northern Ireland.
This could be an area where he looks to build on the policies of the Starmer government, which was in the process of extending regional mayors beyond the main urban areas in England.
Water and energy. Burnham has said he wants all parts of the UK to take "greater public control" of the water and energy sectors. He has suggested this could emulate Greater Manchester's bus network, where private operators bid to run services on a franchise basis, with local authorities controlling fares, timetables and routes.
Housing. Burnham has promised the biggest council house building programme "since the post-War period" - implying a large rise in rates of construction compared to recent years. However, he is yet to offer details of how this would be funded.
He has also called for the entire 10-year £39bn affordable housing budget for England towards homes for social rent, the cheapest and most heavily subsidised form of publicly-funded housing.
Currently some of the budget goes towards "affordable" housing, where rents are more similar to market rates, as well as affordable home ownership schemes. Some of his other policies in this area - including restricting Right to Buy - have already been put in train by the current government.
Personal taxes. Burnham has said he would stick to Labour's pledge at the last election not to raise the main rates of income tax, VAT or National Insurance, whilst maintaining there is "some room within that manifesto for movement" in other areas. During his campaign to be re-elected an MP, he also said he wanted to "have a proper look" at potentially raising the £12,570 starting threshold for income tax.
Burnham has previously argued the UK overtaxes work and undertaxes wealth, prompting speculation he could raise capital gains tax - paid on profits made when selling assets such as shares and property aside from a main home. In one interview, Burnham did not rule out a wealth tax.
He has previously suggested that both council tax and stamp duty, a tax paid by homebuyers, could be replaced with a new tax on the value of land - an idea he has been advocating since as far back as 2010.
Social care. Burnham has long supported the idea that social care should become a more universal system. In a speech in 2023, he suggested this could be funded by replacing inheritance tax with a new "national care levy". He has suggested everyone would pay this new tax, whilst "obviously the wealthiest would pay the most". Labour promised to overhaul the system in opposition, but upon taking office commissioned a review of funding that is not due to report until 2028. Burnham has said he would bring that forward to the end of this year.
Immigration. Like the Sunak government, Labour has reduced levels of immigration by tightening visa requirements. During his Makerfield campaign, Burnham said net migration "needs to fall further", although he has not set a specific target. One area where he could have an internal battle on his hands is over proposals to lengthen the time that foreign nationals already living in the UK would have to wait before they can qualify for permanent residence. Earlier this year, Burnham urged Labour MPs to heed warnings from the party's former deputy leader Angela Rayner about the impact of the changes. But when running to be an MP himself, he said he supported the "broad thrust" of the plans, unveiled earlier this year by Home Secretary Shabana Mahmood.
Welfare and employment. Burnham has said he wants to see a "fair and lasting" reduction to the UK's welfare bill, amid rising spending on health and disability benefits in recent years. But he has not set out plans to change the level of benefits payments, or how people qualify to receive them.
Instead, he argues the claimant count can be reduced by improving employment support and "in-work" mental health support. He has also said he wants 16 to 18-year-olds to have guaranteed work placements. Burnham has said he would keep the "triple lock".
Business policy. Burnham has said he wanted to preserve "sovereign manufacturing" capability in key areas such as steel, defence, energy, and farming, and he wanted to make it easier for British companies to win public contracts. During the by-election campaign, his team sent out a policy document promising a cut in business rates for pubs and music venues by 20%. That would be paid for, they said, by higher taxes of out-of-town warehouses used by online retailers like Amazon. Burnham also wants to raise the threshold at which business rates kick in, taking lots of small high street shops out of paying altogether.
Foreign policy and defence. Burnham has said he would like the UK to rejoin the EU within his lifetime, but he has insisted he does not want to "re-run the [2016] referendum now". He has pledged to seek a "closer relationship" with European countries, and "consolidate the progress made" on existing negotiations with the EU.
Defence spending, which prompted the resignation of Starmer's defence secretary John Healey earlier in June, would provide another headache. In one of his final decisions in office, Sir Keir announced a plan to increase military spending by £15bn over the next four years by cutting spending in other parts of government, whilst leaving the details to Burnham to flesh out.
Electoral reform. Burnham has said he would "seek to persuade my own party" of the need to include a pledge in Labour's next election manifesto to replace the UK's first-past-the-post system with a form of proportional representation.