The 7 May elections are taking place against a backdrop of “war on two fronts”, Keir Starmer has said, as he pledged action to tackle the resurgent cost of living crisis.

Launching Labour’s English local elections campaign in Wolverhampton on Monday, the prime minister said: “We’re facing a war on two fronts – the Ukraine war, now four and a bit years in … and now the Iran war, which I know is causing huge concern.

“People look at their screens and they’re worried when they see explosions, infrastructure blown up, the rhetoric that goes with it, worried about whether this is going to escalate even further.”

Labour is braced for heavy losses in English council votes on 7 May, in particular in the north-east and London, amid challenges from Reform UK on the right and the Green party on the left. The contests are seen as a major test for Starmer’s premiership. There are also national elections in Scotland and Wales.

After 27 years of Labour government in Wales, several surveys suggest voters want change and that the contest for the next Senedd is a two-horse race between Plaid Cymru and Reform UK, with Labour in a distant third. Starmer’s unpopularity also looks set to deny Scottish Labour’s Anas Sarwar a chance of victory over the incumbent Scottish National party in Holyrood.

Starmer said Labour was going out into the English campaigns “on the front foot” and “relishing the opportunity to go to doorsteps and say to people: vote Labour for the following reasons: vote Labour because of our values, vote Labour because of our leadership, vote Labour because it makes a huge difference to so many lives across the country.”

He stressed his party understood that “whatever is going on in the world, whatever is going on in politics, and there’s a lot in both, most people are concerned most of all about the cost of living”.

UK-wide measures announced by Starmer on Monday to help with soaring costs caused by the latest round of fighting in the Middle East include a lower energy price cap and an increase in the minimum wage – moves Labour hopes will stem the party’s haemorrhaging support.

At Welsh Labour’s manifesto launch in Swansea, held at the same time Starmer was speaking in Wolverhampton, the party’s leader, Eluned Morgan, pledged to freeze income tax rates if re-elected, saying “times have been tough enough already”.

Morgan said people wanted “a little more certainty. A little more stability. A little less dread about the next bill or the next news story.”

At Reform UK’s Wales manifesto launch this month, Nigel Farage suggested the Senedd election would be viewed as a referendum on Starmer’s leadership. Morgan has previously sought to distance her government from the Labour administration in Westminster, but she offered her support to the prime minister earlier this year after calls for his resignation, including a high-profile demand from Sarwar.

Also in Wales on Monday morning, Plaid Cymru launched its bid to form the first non-Labour-led administration in Cardiff Bay since devolution began in 1999. Speaking at the Senedd campaign launch in Bedwas, near Caerphilly, the Welsh nationalist party’s leader, Rhun ap Iorwerth, called the 7 May vote the “most important election in the history of devolution”.

“Labour’s time is up – they are now out of the picture. This campaign is a straight choice between Plaid Cymru and Reform, between hope and division, between credibility and chaos,” he said. “7 May is an opportunity to choose new beginnings for Wales, new ideas, a new energy, a higher level of ambition than ever before.”