The rival groups challenging to lead the leave campaign in the EU referendum are to submit their formal applications to the elections watchdog.

The Electoral Commission is charged with designating the lead campaigns for leave and remain, with the chosen teams enjoying major advantages in spending, campaign broadcasts and sending information via post.

While it is expected that only Britain Stronger In Europe will apply for the remain designation, leave is being bitterly contested by Vote Leave and Grassroots Out.

Both campaigns have emphasised their cross-party support. Vote Leave is backed by Conservative figures such as the London mayor, Boris Johnson, Michael Gove, Chris Grayling, John Whittingdale, Theresa Villiers and Iain Duncan Smith.

Grassroots Out has stressed its popularity across the country, staging a series of rallies and claiming to have the support of 2.7 million people, including 2,000 local councillors.

It has the backing of Conservative, Labour and DUP MPs, as well as the Ukip leader, Nigel Farage and millionaire Ukip supporter Arron Banks.

In deciding between them, the commission will look at the breadth of support each campaign has, how it intends to get its message across to voters and how it plans to engage with other campaigners on the lead side.

The commission must announce its decision by 14 April at the latest.

David Cameron said Britain Stronger in Europe had support “from every corner of the UK” and from backers of each of the main parties, as well as those who support no party.

“By contrast, those campaigning to leave the EU are divided into at least two camps, who can’t agree on very much,” he said. “In fact, the only common ground is their inability to tell the British people what would happen if we left the EU. They have failed to answer reasonable questions about what would happen to jobs, prices or our country’s security if Britain left the EU.”

Britain Stronger In Europe has released a study from the London School of Economics which, it said, calculated that prices in the UK were £200 less a year per household due to EU free trade agreements, saving the UK £5.3bn a year.

The report also estimated that future EU trade agreements with the US and Japan would be worth an additional £238 a year to households in the form of cheaper prices.

The claims were challenged by Robert Oxley, a spokesman for Vote Leave, who said independent research had shown that the EU increased costs for consumers.

“That’s on top of the £350m we all have to fork out for Brussels each week,” he said. “The EU has been very bad at negotiating free trade deals, hurting jobs and the economy. That’s why it’s safer for Britain to take back control of negotiating its trade deals so it can prosper outside of the EU.”