More than 2.5 million disposable cups have been bought for use in the Environment Department in the past five years, equivalent to almost 1,400 a day, figures show.
Freedom of Information requests by the Liberal Democrats also reveal the House of Commons catering team have purchased more than 3.9 million disposable cups since 2013.
The figures come amid growing pressure to tackle waste from the "throwaway society", with calls from environmentalists to introduce measures such as a bottle deposit return scheme to cut plastic going into the oceans.
The Liberal Democrats want the Budget to include a charge on disposable coffee cups, which are not easily recycled because of the plastic lining that makes them waterproof.
They point to the success of the 5p charge on plastic carrier bags, which saw the number of single use bags being handed out fall 85%.
Chancellor Philip Hammond is expected to announce a call for evidence on taxing and charging single-use plastics such as packaging and polystyrene takeaway boxes in the Budget, while Environment Secretary Michael Gove has said he wants to tackle plastic waste.
Figures obtained by the Freedom of Information request show that catering and facilities contractors for the Environment Department (Defra) purchased 516,000 disposable cups in the last year alone, for use across the department's offices.
The contractors started trialling the use of plastic "keep cups", which can be purchased by staff and then reused, at the end of October, after the FOI request was received, and has bought 200 such cups for the scheme.
The Commons has also introduced reusable cups, purchasing 500 in 2013, of which 440 have been sold.
They appear to have been initially popular, with 358 bought in the first year, but only four have been purchased since 2015, the figures show.
Liberal Democrat environment spokesman Tim Farron said: "It's astounding that the department which is supposed to be protecting our environment is responsible for such a colossal amount of waste.
"Millions of plastic cups have been thrown away by the Government, some of which will now be polluting our seas, rivers and countryside.
"Michael Gove needs to get his own house in order. A coffee cup charge should be introduced in the Budget to tackle waste and encourage the use of reusable cups, including in the civil service and Parliament."
A Defra spokesman said: "We are committed to reducing unnecessary waste within the department and these figures show the number of disposable cups used has fallen by more than half since 2013.
"We are working with our suppliers to see what more can be done to further cut their use and promote recycling."
A Defra working group has launched a call for evidence on how deposit return schemes for plastic bottles and other drinks containers could work in England, and will be looking at other types of common litter such as takeaway packaging, which could include coffee cups.