The MPs say the charge would lead to 750 million fewer disposable cups being discarded as litter, incinerated or sent to landfill, and would generate £438m.
"The revenue should be used to invest in reprocessing facilities and 'binfrastructure" to ensure that the remaining disposable cups are recycled'.
If an effective recycling system is not established and achieves high levels of recycling by this date, the Government should ban disposable coffee cups.
Creating the paper cups to feed the world's burgeoning coffee house culture sees some 6.5m trees felled every year.
"We only get one or two of them, as they're so hard to recycle due to their plastic coating, which has to be treated differently", Carol said.
Coffee shop owners are under mounting pressure to do more to stop that from happening. "Legislation needs to set a date after which the continued production of unrecyclable coffee cups is banned by law".
"We're calling for action to reduce the number of single use cups, promote reusable cups over disposable cups and to recycle all coffee cups by 2023". Costa is also collecting cups from rival brands in its shops.
The news follows hot on the heels of Pret A Manger's announcement that it will give reusable cup holders 50p off hot drinks from this month.
Britain produces 30,000 tonnes of coffee cup waste each year.More news: NDSU ends JMU 26-game winning streak for sixth FCS Championship
"It is unacceptable that coffee sellers are perpetuating customer confusion though their use of recycling labels and emphasis on the recyclability of coffee cups, despite the shockingly low recycling rate", the report said.
Starbucks has also today announced a trial in London to introduce a 5p charge on disposable coffee cups.
"I am an expert in making fantastic coffee, but they (the cup manufacturers) are the ones with the knowledge and resources to be able to change". The firm sells them for £1 and also offers a 25p discount for customers who bring their own.
Green Party lawmaker and EAC committee member Caroline Lucas told the Thomson Reuters Foundation that the reforms were "long overdue" and hoped that they would change behaviour.
The money raised from those who refused would be used to increase the number of recycling plants able to handle plastic-lined take-away cups.
A 5p charge on coffee cups was first proposed by the Liberal Democrats after it emerged previous year that only one in 400 was being recycled. "The government must do the same and introduce the levy as soon as possible".
Additionally, it said that producers needed to pay more for packaging that proved hard to recycle, and that labeling needed to be improved so that consumers knew how to properly dispose of their cups.
However, some customers have complained on social media that they have seen baristas measuring drinks in disposable cups and then tipping the drink into a reusable vessel - negating the whole point of the exercise. The recycling process is complex, as it consists of separating a thin plastic layer from paper, and most recyclers don't have the ability to do this.