It is estimated that every year in the UK, 2.5 billion coffee cups are thrown away and only one in 400 of these recycled.
Catherine Bearder says, "Many of these discarded cups litter our streets, lay as waste in the countryside and even end up floating in the oceans."
She points out that, in coalition, the Liberal Democrats with the support of the Conservatives introduced a 5p charge on plastic bags.
"As a result, single-use plastic bag use has fallen by more than 85% per cent from seven billion to around 500 million."
The ALDE group deputy adds, "This has had a positive impact on our natural environment and raised significant funds for charities."
She goes on, "As part of the circular economy package, the EU has set a common target for EU countries to recycle 75 per cent of all their packaging waste by 2030."
Bearder has now written a letter to Leadsom urging her to address the problem.
It reads, "I urge you to consider introducing a similar policy in our nation's coffee outlets. Customers should be rewarded for using reusable coffee cups and efforts must be made to make single-use cups recyclable.
"The EU has set a common target for EU countries to recycle 75 per cent of all their packaging waste by 2030. The UK must endeavour to meet these targets. When we leave the EU it is very important that Great Britain's environmental standards do not decline."
She adds, "I hope you will consider this environmental problem carefully and implement a solution as soon as possible."
Speaking separately, Bearder commented, "This level of waste is simply unacceptable, the government must take action to clean up this mess.
"The success of the 5p plastic bag policy shows how with some incentive we can overcome big environmental problems.
"It is really important the UK does not drop its environmental standards following Brexit. We must work hard to meet the recycling targets set by the EU."