The coffee chain has announced that between 20 to 25 London stores will trial the scheme for three months starting in February after it learned Parliament's Environmental Audit Committee would propose a "latte levy" on disposable cups today, according to The Times.
The committee is calling on the Government to introduce a 25p levy on disposable coffee cups, and wants all coffee cups to be recycled by 2023.
Many consumers believe the paper cups used by coffee chains can be more easily recycled than they actually are. However, the cups feature a thin plastic film that makes recycling difficult.
If the target of recycling all cups is not reached by 2023 then the committee recommends the Government should ban all disposable coffee cups.
The committee is proposing the levy because consumers are more responsive to a charge than a discount for reusing cups.
Some coffee shops provide discounts for customers who bring their own cup (Starbucks for example gives back 25p) but uptake of these offers is low at only 1-2% of coffee purchases.
The levy has also been partly inspired by the success of the plastic bag charge, which has reduced plastic bag usage by over 83% in the first year.
Environmental Audit Committee chair Mary Creagh MP said: "The UK throws away 2.5 billion disposable coffee cups every year; enough to circle the planet five and a half times. Almost none are recycled and half a million a day are littered.
"Coffee cup producers and distributors have not taken action to rectify this and Government has sat on its hands. The UK’s coffee shop market is expanding rapidly, so we need to kick start a revolution in recycling.
"Coffee shops have been pulling the wool over customers’ eyes, telling us their cups can be recycled, when less than 1% are."
No other major coffee retailer yet appears to be following Starbucks' lead on trialling a surcharge.
Pret A Manger this week raised its discount for customers bringing their own cup from 25p to 50p after positive feedback to its chief executive Clive Schlee's proposal to do so on Twitter in November. A spokesperson said the chain also plans to offer a reusable cup later this year.
McDonald's said in a statement: "We are committed to reducing our environmental impact and continue to challenge ourselves and our supplier partners to help evolve our thinking, and this includes the recycling of coffee cups.
"Since 2015, we have been installing recycling units which can now be found in over 1,000 of our UK restaurants, enabling our customers to easily separate paper cups from other waste packaging in order for them to be recycled.
"We look forward to the government’s response to the committee’s recommendations, and hope to be able to work together on a scheme that will reduce disposable coffee cup waste, which will work for our customers, restaurants and environment."
Costa said: "Through our nationwide in-store recycling scheme we have recovered over 12 million cups for recycling since February 2017 but understand the serious need to ensure better infrastructure is available outside of our stores. To encourage our customers to use reusable cups we already offer a 25p discount, which we will be further promoting this year.
"We believe the Government must consider a mix of measures to address this issue with a focus on improving the UK’s waste and recycling infrastructure."