It has branches in Swindon, Chippenham, Devizes and Marlborough, although the affected branches have not been named.
The moves comes as part of a major restructuring plan by the company.
What have Pizza Express said?
The chain said it is planning to launch a company voluntary arrangement (CVA) in the “near future” in a bid to push down its rents amid a “significantly more challenging environment” after the coronavirus pandemic.
The outcome has “yet to be decided”, Pizza Express said, but it may end in the closure of about 15 per cent of its 449 restaurants in the UK, affecting 1,100 staff.
The company added: “This decision is a very difficult one; however, against the current unprecedented backdrop, Pizza Express believes reducing the size of its estate will help it to protect 9,000 jobs.”
Pizza Express will put itself up for sale
Pizza Express also said it had put itself up for sale after bringing in experts.
The sale will be run independently to its other plans and was started on Tuesday, Pizza Express revealed.
Separately, it announced plans to sell its business in mainland China and has brought in restructuring experts to help deal with its £735 million debts.
UK and Ireland managing director Zoe Bowley said: “While the financial restructuring is a positive step forward, at the same time we have had to make some really tough decisions.
“As a result, it is with a heavy heart that we expect to permanently close a proportion of our restaurants, losing valued team members in the process.
“This is incredibly sad for our PizzaExpress family and we will do everything we can to support our teams at this time.
“As we continue to reopen our restaurants for dine-in and delivery, we will successfully navigate the extended period of social distancing expected in the months ahead and, in so doing, protect 9,000 jobs.
“The initial signs from the restaurants that have been reopened have been very encouraging and we hope that our loyal customers continue to support us now more than ever.”