Pret a Manger and Wagamama have become the latest companies to announce an end to automatically providing plastic straws.
Customers will be offered a paper alternative, and plastic straws will be available only on request.
The firms' decision comes after Theresa May called plastic waste one of the "environmental scourges of our time".
According to trade organisation Plastics Europe, the UK uses 3.7 million tonnes of plastic a year.
A study by Eunomia Research & Consulting estimates that EU countries use 36.4 billon straws each year.
Pret a Manger - a food outlet with more than 300 stores in the UK - said plastic straws would be kept behind the tills and paper straws would be available to their customers in some stores from next week.
Pan-Asian restaurant chain Wagamama has more than 100 branches in the UK and its chief executive Jane Holbrook said: "We are constantly looking to make improvements and reducing the amount of non-recyclable waste we produce."
The company's policy comes into force on Earth Day - 22 April - which is a global event aimed at promoting activities that protect the environment.
Friends of the Earth waste campaigner Julian Kirby welcomed Wagamama's announcement, saying: "This is significant step in the right direction, but we need far bigger strides from government, industry and retailers to properly tackle the scourge of plastic waste."
In September last year, pub chain JD Wetherspoon said it would be providing paper straws rather than plastic ones in its bars.
McDonald's has said that its straws are made from recyclable plastic and that it is exploring ways to reduce straw consumption.
Supermarkets are also making changes to reduce the amount of plastic they produce.
Earlier this week, the supermarket Iceland said it would eliminate plastic package on its own-label products by 2023.
Tesco aims to make all its packaging recyclable, and Sainsbury's wants to halve the amount of packaging it uses by 2020.