Restrictions on social gatherings are to be brought in across Northern Ireland in an effort to bring coronavirus under control, the first minister, Arlene Foster, has announced.

The entire population is being told they must avoid mixing indoors with people from another household, with some exceptions, while no more than six people from two households will be able to meet in private gardens from 6pm on Tuesday.

“The virus is everywhere and will spread everywhere, and hence our advice is that generalised restrictions are required,” said Stormont’s chief scientific adviser, Prof Ian Young. “We believe this is a proportionate response to the increased number of cases, focusing on the settings where most cases seem to be acquired at present.”

Single-person household bubbles will be exempt from the new restrictions and there will be further exemptions for those with caring responsibilities and other circumstances. Similar restrictions were already in place in Greater Belfast and Ballymena in Country Antrim and these are being extended to cover all of Northern Ireland’s nearly 2 million people.

That follows the announcement that about a quarter of the Welsh population will be subject to local lockdowns after sharp rises in Covid-19 cases. Restrictions on travel and socialising will come into force from 6pm on Tuesday across Newport, Bridgend, Merthyr Tydfil and Blaenau Gwent in south Wales.

Announcing the extension of the measures in Northern Ireland, Foster said: “It is in an environment where we feel safe and relaxed that we drop our guard. The mixing of households indoors provides one of the best opportunities for the spread of the virus.”

She added: “This is not returning to lockdown. Doing nothing was not an option but neither is returning to full lockdown. These are limited restrictions which I hope by taking action at this early stage means we can prevent the need for more draconian measures.”

Between 2% and 4% of tests are positive and show increased community transmission, Young said. He added that the virus’s reproductive rate had risen to 1.4 and in some local districts would be about two. In the last 48 hours nearly 400 new cases have been reported amid “substantial” increases across Northern Ireland, Foster said.

Despite that, pubs that do not serve food will open on Wednesday because Young said it had proven possible to put in safety measures at hospitality outlets that do not exist in private homes.

The deputy first minister, Michelle O’Neill, said people were “fed up and tired” with Covid but that it posed a real threat and they had the opportunity to prevent an even more challenging situation this winter.

“Covid-19 has been allowed to get a foothold in our community and we need to take action now,” she said. “This is a fightback – the months ahead will be difficult.”

House parties in south Belfast’s Holyland student district and a pitch invasion by Gaelic Athletic Association sports fans have caused concern over recent days.

The news that all people in Northern Ireland are to be banned from visiting each other’s homes will bring the number of people under some level of restriction in the UK to 15.4 million – or 23.1% of the population – from Tuesday.

More than a quarter of the population of Wales (27%) is under local lockdown and a third of Scotland’s population reside in the seven local authority areas still covered by restrictions. A full list can be found here.

Foster suggested some people had lost their self-restraint as she warned them to comply with the restrictions. “Whether they ran on to the pitch at a GAA match, partied in bars afterwards, swarmed the streets of Belfast Holyland or indeed crowded into house parties, that kind of behaviour isn’t just a risk to those present, but of course for everyone they subsequently come into contact with.”

The DUP leader said a Stormont enforcement group was examining how to clamp down on such behaviour. “I’m putting you on notice that we intend to take this matter very seriously,” she said.