Mr Johnson has touted April 12 as the date that pubs and restaurants will be permitted to serve customers sitting outdoors.
The Water Lane Boathouse pub in Leeds said on Wednesday that they had received over 700 bookings in just five hours
“Please bear with us as we work our way through them,” it told customers on Twitter.
Since the announcement, industry group UK Hospitality has said many pubs have reported “strong interest from customers” ahead of the much-anticipated date.
"Our members that can open outdoor areas have reported strong interest from customers, which is not surprising after such a long period of closure," said Kate Nicholls, chief executive of UK Hospitality.
Burger chain Byron has confirmed it will reopen 17 branches from April according to The Sun.
They said they have also seen a surge in bookings following the prime minister’s announcement.
"Bookings will not be mandatory, although lots of venues will probably implement a booking system," said Ms Nicholls.
"Businesses will have their own systems in place for managing high demand, processing bookings and ensuring high levels of safety are met".
Ms Nicholls added that while the hospitality industry will only see a slight change in April, many businesses don’t have outdoor areas and the industry will still face challenges.
"April isn’t going to represent a reopening of any significance, or a reopening at all, for much of the sector. We need to remember that nearly 60 per cent of hospitality businesses don’t have outdoor areas and many that do only have small spaces".
From May 17, restaurants will be allowed to offer indoor seating to diners from two households or groups of up to six people.
Limited crowds will also be allowed at sporting events.
From June 21, all remaining restrictions on social contact could be lifted, meaning larger events will go ahead and nightclubs could finally reopen.