The US firm said it would trial a 5p charge on its cups at up to 25 of its London coffee shops in wake of the MPs' report.
The government should also ensure that all disposable cups are recycled by 2023 or introduce a total ban if that target is not met, an Environmental Audit Committee (EAC) report found.
The Committee's report also recommends that all single-use coffee cups are recycled by 2023, and if this isn't in effect by then that there is an outright coffee cup ban.
It's not just MPs making plans to tackle the issue of coffee cup waste. The plastic lining in cups makes them very expensive to recycle, and the businesses who are responsible for handing them to customers pay just 10% of the bill for dealing with the waste packaging!
She added: "With the coffee shop market expanding rapidly, and more coffee cups being produced, we now have the opportunity to kick start a revolution in recycling".
At least 2.5 billion disposable cups are thrown away every year.
The committee said it was "disappointed" that only Costa and Starbucks provided written evidence for its investigation, and not other major retailers, including Caffe Nero and the supermarket chains Tesco, Morrisons and Pret a Manger. The charge on disposable cups would be paid by consumers on top of the price of their coffee, and would be lowered as the recycling rate improves, it said. The trial will begin next month and initially last for three months.
If all disposable coffee cups are recycled by 2023, that will require a lot of infrastructure - there are only three recycling facilities in the United Kingdom that can split the paper from the plastic for recycling at present (which is why less than 1% of cups are recycled). It's also been suggested that the cups be phased out, with a full ban by 2023.
"Finally, we will continue to remind customers through our in-store marketing about the ongoing 25p cup discount and the benefits of going reusable".
"If the proposed levy were to be introduced, we believe it should be used to fund the collection of cups, since once they are separately collected they have a value and can be made into new products".
"The whole point is to change behaviour and I'm glad the select committee has endorsed this Liberal Democrat campaign", he said.
Other measures recommended by the committee include producers paying more for packaging, and improved labelling so consumers know how best to dispose of their cup.
Numbers of the throwaway cups have hugely increased in recent years.
"By singling out disposable cups the committee is, by its own admission, looking for United Kingdom coffee retailers and their cup providers to underwrite the waste management of all packaging used on the go", he said.
The government now follows targets set by the EU Waste Directive for recycling paper and plastic, but none refers specifically to the mixed-material cups; moreover, there are no confirmed targets in place for once the United Kingdom leaves the European Union.
And sceptics should remember the impact of the 5p charge on single-use carrier bags.