According to the BBC, Treasury estimates put the average claim at close to £5, making the cost of the policy around £50m so far.
HMRC said that, as of last Sunday (9 August), it had received 10,540,394 claims under the scheme.
Chancellor Rishi Sunak described the figures as "amazing", adding those using the scheme were helping support the hospitality sector.
The Government has set aside £500m to fund the policy.
The scheme, which launched last week, is aimed at protecting jobs in the hospitality industry and encouraging people to safely return to dining out.
Restaurants, bars, cafes and other establishments who use the scheme will offer a 50% reduction, up to a maximum of £10 per person, to all diners who eat and/or drink-in on Mondays, Tuesdays and Wednesdays throughout August.
It can be used by diners who order food and/or drinks for consumption on the premises, however, alcohol is excluded from the offer.
According to the most recent HMRC figures, 83,000 restaurants across the UK have now signed up to participate in the initiative
Following its first week, chefs and restaurateurs including Hawksmoor co-founder Will Beckett and chef Tom Kerridge hailed the initial success of the scheme as an important first step in giving consumers confidence to return to restaurants.
“Although we’ve seen lower sales due to the lower spend per head, but we’re still incredibly happy – everyone loves having busy restaurants and lots of new people are coming in and trying Hawksmoor for the first time, or finding a way to come back that they can afford at the moment," said Beckett, whose restaurant group has received more than 15,000 bookings across its six restaurants between Mondays and Wednesdays in August.
"Anything that encourages people to leave the home and start enjoying restaurants again is great.
"The industry needs this kind of kick-start at the moment.
"I think it is a really good example of much-needed government intervention for an industry still in crisis.”