Valentia Slate Ltd has secured a 10,000 contract to supply the slate.
The original floors, which were laid in the middle of the 19th century, also contain Valentia slate.
The quarry on the picturesque island, off south Kerry, was internationally famous, and was re-opened by a company formed by three local businessmen, in 1998. It had been closed since 1911.
Ten people are employed by the company, which has invested 500,000, and business is growing, said director Michael Lyne.
“We regard our latest contract as very prestigious and it should be the first in a series of orders from the Palaces of Westminster,” he said yesterday.
“We’re delighted to see our slate replacing some of the old slate that was quarried in an era when Valentia slate was in great demand. More than 400 people were employed in the quarry in the 1860s,” said Mr Lyne.
The company, which has won a Kerry Enterprise Award, has a wide range of products, including kitchen and bar counters, flooring slabs, fire-surrounds, hearthstones, mantelpieces, wall capping, crazy paving, roofing slates, building stone, garden furniture, gravestones, window-sills and lintels.
Valentia slate is also in demand for modern architectural works and has been used in the national heritage restoration buildings.
The quarry is believed to be the only one of its kind operating in Ireland.
First opened, in 1816, by the Knight of Kerry, it was run by various companies until 1911 when a rockfall at the mouth closed the mine.
Its slate products included roofing slates, flooring slabs, fire-surrounds, snooker tables, sills, lintels, water troughs and steps.
The slate became internationally renowned and was used in Westminster Abbey, Westminster Cathedral and St Paul’s Cathedral.
It was also used in 21 miles of shelving in the Public Records Office in London.
It also featured in the Paris Opera House and in many of the main underground railway stations in London, including Waterloo, Charing Cross and Black Friars, and as railway sleepers in San Salvador Railway, South America.