The government scheme offers customers 50% off their meal, up to a maximum of £10 during August.

But chains such as Prezzo, Harvester and Pizza Pilgrims now say they will offer the discount next month too.

The aim is to draw people nervous about coronavirus back to restaurants at a time when many are struggling.

Some 84,000 restaurants, cafes and bars have signed up to the government's scheme, which runs on Mondays, Tuesdays and Wednesdays in August.

According to the latest Treasury figures, diners used it more than 64 million times in its first three weeks - equivalent to nearly every person in the country dining out.

Commercial landlord Grosvenor - which owns property across central London - said it would reduce rents for tenants that continue to offer diners half-price meals until the end of September.

High end restaurants Comptoir and Roka, the Thomas Cubitt pub and Peggy Porschen café are among those to sign up.

"Eat Out to Help Out has been a powerful tool in protecting jobs and local economies UK-wide and we are working hard to help the West End and our tenants recover," said Amelia Bright, executive director of Grosvenor's London estate.

"Continuing it will not only support cafes, restaurants and bars that we lease space to but also help welcome back more visitors and workers to Mayfair and Belgravia."

Others say they will offer different discounts inspired by the scheme.

Spanish City, a steak and seafood restaurant in Whitley Bay, told the BBC it would offer a 25% discount on all food and non-alcoholic drinks on Monday to Wednesdays, with no cap on spending.

Industry in crisis

About 80% of hospitality firms stopped trading in April and 1.4 million workers were furloughed - the highest proportions of any sector - according to government data.

Industry body UK Hospitality says around a third of restaurants and bars have still not reopened despite the easing of lockdown, as people remain nervous about the spread of the virus.

Boss Kate Nicholls welcomed the move by individual restaurants to extend the Eat Out scheme, saying it had been "a huge success".

"The hospitality sector is still fragile and faces other challenges, but prolonging the Eat Out scheme could help businesses back to stability and enable them to safeguard jobs and livelihoods," she said.

A growing list of restaurant chains have had to announce closures in recent months including Pizza Express, Byron Burger and Frankie & Benny's-owner the Restaurant Group.

And on Wednesday, Mexican chain Wahaca said it was closing 10 of its 25 restaurants, and that it would "try to save jobs" wherever possible.

Spanish City's operations director Rob Smith told the BBC the Eat Out scheme had boosted its sales, but he remains cautious.

"We're forecasting being down about 25-30% for the rest of the year, and we're having to catch up on the three months we lost out - it's still very nervous times for the industry."

Here is a list of the restaurant chains which have confirmed to the BBC they will offer Eat Out to Help Out discounts in September:

Nationwide:

Pizza Pilgrims

Harvester

Toby Carvery

Stonehouse Pizza

Carvert

London

Burger & Lobster

Popina

The Mayfair Chippy

Roka

NAC (north Audley kitchen)

Comptoir

Prezzo

Kai

Horse & Groom pub

Pantechnicon

l'ETO London

Boisdale

Jones Family Kitchen

Hunan

Peggy Porschen

La Poule Pot

The Duke of Wellington (pub)

UNI Restaurant

Shack-Fuyu

Flesh & Buns

Arabica

José Pizzaro

Benares

Kricket

Paladar

Sticky Mango

BOXPARK

Pasta Remoli

Aqua Kyoto

Aqua Shard

Hutong at the Shard

The Gilbert Scott (St Pancras Renaissance Hotel)

Saffron Circle

Cecconi's Pizza Bar, Soho

Cafe Boheme, Soho

The Allis, White City

Electric Diner, Portobello

Pizza East, Shoreditch

Dean Street Townhouse, Soho

Hoxton Grill, Shoreditch

The Midlands

House of Darwin

Hurt Arms

White Hart

Horse & Jockey

The Beech House

The Akeman

The Anchor Riverside

Banyers House

The Betsey Wynne Swanbourne

The Blue Boar Witney

The Cherry Tree

The Crown & Whistle

The Four Alls

The Globe

Kings Arms Berkhamsted

The King's Head

The Lost Boy

The Navigation Inn Thrupp Wharf

The Old Post Office

The Penny Farthing Hotel

The Polecat Inn

Red Lion

Royal Foresters Ascot

The White Hart Ampthill

Tyne and Wear

Spanish City

Glasgow

The Anchor Line (1-2 Sept only)

Atlantic Bar & Brasserie (1-2 Sept only)

The Citizen (1-2 Sept only)

Cafe Andaluz (1-2 Sept only)

Di Maggio's (1-2 Sept only)

Belfast

Deanes