All major British theatre will cease and several cultural institutions will close or postpone shows as the impact of the Covid-19 pandemic on the UK’s arts and culture sector grows following the government’s call for “drastic action” to halt its spread.

The Society of London Theatre (Solt) and UK Theatre, the industry body that represents nearly every British theatre, announced that, as of Monday night, all its members would close their doors. The groups represent about 50 London theatres and almost 250 others throughout the UK.

Julian Bird, chief executive of Solt and UK Theatre, said the decision would have a “severe impact” on many of the 290,000 individuals working in the industry, and encouraged theatregoers to consider donations in order to help the sector. “Those who can afford to do so are encouraged to donate the cost of their ticket to show support for the theatre industry,” he said.

The announcements came shortly after the prime minister, Boris Johnson, said people should avoid pubs, clubs and theatres as he set out the need for “drastic action” to tackle the fast growth of coronavirus across the UK.

Earlier, several cultural institutions in the UK, including the Institute of Contemporary Arts and the National Gallery, confirmed that they were taking the “unprecedented” step of closing or significantly reducing their offering, with some turning to online alternatives for those unable to attend physical spaces.

The National Gallery confirmed on Monday that it would postpone its Artemisia exhibition, which was due to open on 4 April. In a statement, the director of the National Gallery, Dr Gabriele Finaldi, said the decision was taken for “logistical and organisational reasons” caused by Covid-19. On Monday evening, the gallery confirmed it would “operate as normal, but would continuously and closely monitor the situation”.

The ICA director, Stefan Kalmár, confirmed that it would close temporarily and said he hoped all cultural organisations in London and the UK would follow suit in order to “safeguard staff, visitors, and the artists with whom we work”.

The theatre world offered online alternatives as some productions closed early with huge financial implications. The Old Vic’s Beckett revival, Endgame, starring Daniel Radcliffe and Alan Cumming, closed two weeks early. The theatre asked customers to consider donating the cost of the ticket rather than requesting a refund because the impact would be “financially devastating”. The Old Vic said it would provide a video link to a full recording of the production and a “friends” membership enabling priority booking for one year to those who contributed.

The Arcola, in east London, suspended all public performances until further notice, with a bleak prediction for “the livelihoods of all those who work in the arts”.

Riz Ahmed’s The Long Goodbye, which was due to debut in Manchester for three nights at the end of March before moving to Brooklyn, has now been postponed until the autumn because of concerns over “the health, safety and wellbeing of audiences, artists and staff”.

South London Gallery was among the first institutions to close, shutting down its Camberwell building over the weekend and postponing all educational programming until further notice, saying it was “monitoring the situation on an ongoing basis”.

Many others are following current government advice and keeping a “business as usual” approach by staying open while continuing to watch for updates.

Tate Modern said it planned to stay open despite a non-front-of-house staff member testing positive for the virus last week. In a statement released last week, it said the people with whom the staff member came into contact with had been traced and all areas with which they have come into contact had been “deep cleaned”. On Monday, Tate said: “The safety of staff and visitors is always our first priority. We are following scientific guidance from Public Health England.”

The UK’s other most popular museums and cultural institutions – Tate Britain, the V&A and the British Museum – will all remain open, despite the closure of their European counterparts, including the Louvre in Paris and the Reina Sofia and Prado in Madrid.

The British Museum, which along with Tate Modern is the most-visited cultural space in the UK, confirmed it was following Public Health England and government advice by staying open, although the situation was “under active review”. The museum said that its online archive was available for free and included virtual reality tours, as well as specialised programmes for schools.

The shutdown of cultural institutions triggered a response from Arts Council England (ACE) to help support vulnerable art practitioners. On Sunday, it announced measures to support artists and freelancers working in the arts, museums and libraries, including the “refocus” of some grant programmes to compensate for lost earnings, although it said firm details on this scheme could take 10 days to be released.

ACE confirmed funding conditions for National Portfolio Organisations and Creative People and Places will not apply for at least three months, meaning institutions that receive money won’t be expected to meet certain targets.

The English National Opera confirmed it would remain open but would offer “credit notes” that could be used to purchase tickets for future performances for those who felt unable to attend. The ENO also confirmed it was developing “online alternatives” should it be forced to close.

Berlin Philharmonic is offering its archive of recorded classical concerts for free online at its Digital Concert Hall after announcing its real-life closure. Other orchestras are hosting livestreams of concerts, including the Bavarian State Opera and Wigmore Hall that is streaming a version of England’s Orpheus on Sunday 22 March.

Commercial galleries in London also announced closures, with David Zwirner saying in order to “prioritise the health and safety of our staff, artists, visitors, and neighbours” its London and Paris galleries would be closed until further notice. That followed similar moves by Sprüth Magers, Michael Hoppen and Olivier Malingue, which confirmed they would close.

In a statement, Zwirner said, “Art can be a balm in uncertain times” and offered virtual exhibitions on its website, following the lead of other cultural institutions in Europe that are offering online alternatives to attending events in physical spaces.

Other cultural events that were cancelled or postponed on Monday include the International Opera Awards, which were due to take place in London on 4 May but have been postponed until 21 September, and the BFI Flare: London LGBTIQ+ film festival, which has been cancelled, as has the Oxford literary festival.