Along with the managed sites, the company's 120 or so tenanted and leased sites are also being strongly encouraged to do the same, with a poster available to all licensees.
The "plastic isn't fantastic" signage explains that plastic straws are no longer being offered with drinks, but eco-friendly paper straws are available on request at the bar.
Brakspear marketing manager Emma Sweet said: "Plastic straws are rightly being seen as a cause of pollution that can be easily eliminated.
"Consumers are keen to reduce their personal plastic use and we've had lots of questions in our pubs.
"Clearly, for our tenants, ditching plastic straws is a decision they have to make about their business, and the poster helps them to explain the policy to customers."
One of the first pubs to order the posters was the Flower Pot in Sunbury-on-Thames, Surrey, run by the Authentic Pub Co.
Co-founder Sarah Bailey said: "Reducing plastic use is a huge consumer movement now and we're keen to do our bit to help, so getting rid of plastic straws was an easy decision.
"We've sourced paper straws through our cleaning supplier and we've ordered the posters from Brakspear.
"The switch has been welcomed by our customers – everyone's on the same page when it comes to plastic, so they're glad to be using more environmentally friendly paper straws."
Last week, the British Beer & Pub Association (BBPA) published guidance on plastic straw alternatives – outlining the various recyclable, reusable and biodegradable alternatives to the single use appliances. The BBPA’s guidance can be found in full here.
Other pub companies to ditch the plastic straw include Oakman Inns, JD Wetherspoon, Ei Group and Punch.
Along with other industry bodies, The Morning Advertiser has launched a campaign to cut the amount of single-use plastic straws used in pubs.