David Cameron has overruled the Home Office and ordered a rethink to ensure that pubs can be open for England's World Cup fixture against Italy.

The prime minister stepped in after pubs were refused permission to extend opening hours for the match on Saturday 14 June, which kicks off at 11pm.

The Home Office had refused a request from the British Beer and Pub Association (BBPA) for an extension of licensing times across the country. But in a message on Twitter, Cameron said: "I have ordered a rethink on pub opening times for England's World Cup games – will consult with pub trade, police and councils."

The pub industry asked the Home Office to delay closing time from 11pm on 14 June to 1am on 15 June across the country to give fans time to watch the game. But Home Office minister Norman Baker turned down the proposal, leaving pubs with the option of applying individually to local authorities for a licence extension.

The BBPA, which represents England's 49,400 pubs, believes the extended opening times could be worth an additional £20m to the industry in drink and food sales.

Ministers have the power to relax the rules to mark an occasion of exceptional international, national or local significance", as was done for the Royal Wedding and Diamond Jubilee.

England's remaining two group-stage games will be played at more convenient times for pubs, with the 19 June clash with Uruguay scheduled for 8pm UK time and the potentially decisive match against Costa Rica for 5pm on 24 June.

If Roy Hodgson's team makes it past the group stage, the remaining fixtures they could be involved in will kick off at 9pm UK time, apart from the final, which will be played at 8pm on 13 July in Rio de Janeiro.

BBPA chief executive Brigid Simmonds said it was a commonsense decision. "This would make for the most fantastic news for thousands of publicans and millions of football fans. I am delighted that the prime minister has intervened."

Cameron's official spokesman said the Home Office will conduct a consultation with interested parties before a final decision is made on whether pubs can stay open late for the England match.

"The Government position is that we are consulting on nationally extending the opening hours as a result of the Prime Minister asking the department to look again at this issue," the spokesman told a Westminster media briefing.

"It is right that we consult but, subject to that consultation, clearly our intention would be that pubs would be able to be open for the relevant games, reflecting the fact that it is a major national event."

A Home Office spokeswoman said: "We will be launching a consultation shortly to determine whether pubs should be able to extend their licensing hours during the World Cup 2014 in Brazil.

"Given the time difference between the UK and Brazil and the fact some matches kick off at 11pm, the consultation will cover late-night matches occurring on the opening weekend, the closing weekend of the World Cup 2014 and for England's 11pm matches.

"We will examine the responses to the consultation thoroughly and carefully before deciding how to proceed thereafter."