Richard was baptised at St Margaret's, Rochester, Kent on 29 August 1757, with his parents named as William and Charlotte.
Richard Twopeny studied at Oriel College, Oxford. In 1781 he was domestic chaplain to Henry, Baron Teynham. In 1783 he was appointed Rector of Little Casterton, Rutland, England. As Rector he contributed substantially to the cost of restorations of the church, and helped to endow a school.
On 10 October 1786 Richard married Margaret Nowell at Iffley, Oxfordshire. Six daughters were known punningly as "the splendid shilling".
In 1819 a bookseller of Stamford, Lincolnshire asked Richard to contribute to the cost of publishing poems by John Clare. Richard replied that the poems had "no merit to be worthy of publication, though I have no objection to assist in raising the poor man a small subscription." Clare responded:
Twopenny his wisdom is & Twopenny his fame is,
Twopenny his merit is & Twopenny his name is,
And as Twopence is a trifle I will do without him,
I’ll sing in spite of Twopences & not care Twopence about him.
Richard died on 23 November 1843 and was buried on 30 November 1843 at Little Casterton, Rutland. His death was registered at Stamford, Lincolnshire in the 4th quarter of 1843.