The appeal, launched by art charity The Art Fund and the organisers of the Olympia International Art and Antiques Fair, is looking to raise £15,000 towards the £300,000 price tag on the painting.
It is hoped the painting can be saved for the museum in Exeter after it was pulled at the last minute from a Christies auction. The subject, John Rolle Walter (1712-1779), was an eminent figure in the South West of England. A landowner and MP for Exeter and Devon, he was painted by the fashionable Italian portraitist whose work is currently showing at the National Gallery.
"This great Batoni portrait is of historical interest because John Rolle Walter was a key figure in the turbulent politics of 18th century Exeter," said David Barrie, Director of The Art Fund, "but what really matters is that it is an artistic tour de force. Exeter must have it and I am sure that visitors to the Olympia fair will rise to the challenge now that The Art Fund has launched the fundraising campaign."
The Olympia Art Fair has been running annually for 35 years, and is on from June 5 to 15 2008.
Fundraising is being carried out through the sale of pieces of a giant jigsaw puzzle replica of the portrait, priced £5 to £1,000, over the course of the fair.