In Hampshire, the Mayflower Theatre in Southampton has cancelled all live performances for this week and next week and will be "dealing with shows on a week by week basis".
The New Theatre Royal in Portsmouth has closed for at least the next 14 days and the Theatre Royal in Winchester has suspended its live performances.
In Sussex, the Brighton Dome has temporarily closed describing it as a "huge blow to arts in the city".
In Kent The Marlowe has announced it will shut for a month.
In Dorset however, most performances and events at the Bournemouth Pavilion are scheduled to run as programmed.
In Oxford, the New Theatre has temporarily suspended all of its shows with immediate effect.
In Berkshire, all events at The Hexagon, South Street, Concert Hall and Reading Museum up to April 18 2020 are being postponed.
Meanwhile, Reading Borough Council has closed all council-run buildings from Tuesday including libraries, leisure centres and the town hall.
Industry leaders have warned firms will go out of business without urgent state help to get through the next few months.
High-profile figures including chefs Simon Rimmer and Raymond Blanc have joined calls for the position to be made clear after the Prime Minister told people to stay away from bars and restaurants but stopped short of ordering entertainment venues to close.
Chancellor Rishi Sunak will set out a new package of support on Tuesday afternoon for businesses hit by the outbreak.
Many have said while they understand the need to protect public health, the lack of an enforced shutdown means businesses cannot claim insurance, a move described by food critic Jay Rayner as "staggeringly reckless".
The British Beer and Pub Association has written to Mr Johnson, demanding urgent steps are taken to prevent mass job losses and permanent pub closures.
The association's chief executive Emma McClarkin said the industry is facing"an existential crisis" as a result of the new guidance, insisting thousandsof jobs will be lost without financial help from the Government.
She said: "Forced pub closures without a meaningful support package will have a catastrophic financial and social impact."
The letter calls for the Government to cancel all business rates payments forsix months, as well as all tax payments including PAYE, VAT and corporation tax for pubs and hospitality businesses.
It also calls for the cancellation of beer duty payments for six months, andthe postponement of the planned national minimum and living wage increases due in April.
At a press conference in Downing Street on Monday afternoon, Mr Johnsonadvised: "You should avoid pubs, clubs, theatres and other such socialvenues."
Asked whether pubs, restaurants and theatres were being ordered to close, the Prime Minister said: "What we are doing is giving very strong advice thatpublic venues such as theatres should no longer be visited."
He said enforcement powers are there if needed, but added: "I don't believe it will be necessary to use those powers."
Mr Johnson added: "We are going to make sure that we do everything we can to give them the liquidity that they need."
A petition calling for the Government to provide clear financial and practicalsupport and to set out a timeline "so businesses can prepare logistically andrationally for times ahead" had gained more than 73,000 signatures by Tuesday morning.