The Drapers Arms in London's Islington is among those to confirm on social media that they will not open today, as is Liverpool-based restaurant group Maray.
In a post on Instagram, The Drapers Arms owner Nick Gibson said the pub would be closed today (Monday) for staff welfare.
"Monday is looking like an unacceptable heat for staff so we're closing on the day," he said.
Gibson added in a separate post that the pub would be open on Tuesday owing to a booking it must honour, but will be working with a cold kitchen.
"I have insisted that the chefs have no hot equipment so think cold meats and fish dishes, light fresh food. We will also limit numbers to control heat."
Elsewhere in London, Laksamania on Newman Street confirmed it would be closed on Monday and Tuesday.
The Met Office has issued a red extreme heat warning on Monday and Tuesday in much of England, from London and the south-east up to York and Manchester.
High temperatures are also forecast across the UK - with amber warnings in the rest of England, all of Wales, and parts of Scotland.
In Liverpool, Middle Eastern-inspired restaurant group Maray has said its site on Bold Street will be closed on Monday and Tuesday, but that its other locations, which includes a recently launched Manchester outpost, will continue to operate.
Writing on Instagram, Maray said: "The reason for shutting this site is that due to the setup and size of the kitchen, it gets very hot in the summer. So with these impending extreme temperatures we believe it's the safest course of action and want to prioritise the wellbeing of the team.
"Our other restaurants have either open kitchens or stronger air inflow systems meaning they are much cooler, and will remain open as usual."
Meanwhile, in Ashby, Leicestershire, Italian restaurant Zamanis confirmed that it too would be closed over the next two days.
"Due to the weather forecast and unprecedented temperatures we have taken the difficult decision to close Zamanis on Monday and Tuesday," the restaurant said in a Facebook post.
"Our staff work so hard at all times and we think it is unfair to expect them to carry on in temperatures of over 60 degrees (in the kitchens). We really hope you understand and we look forward to greeting you again from Wednesday."