The depiction of rural life in Suffolk is tipped to fetch up to £25 million ($40 million).
Baroness Carmen Thyssen-Bornemisza said it was “very painful” to sell the 1824 masterpiece but had to because she had “no liquidity”.
The work has been housed in Madrid’s Bornemisza Museum, one of whose board members has resigned in protest.
Museum trustee Sir Norman Rosenthal criticized the Baroness, known as Tita, for putting one of its prize exhibits up for sale.
In his resignation letter, the former exhibitions director of London’s Royal Academy said the decision “represents a moral shame on the part of all those concerned, most especially on the part of Tita”.
If it fetches its expected price, The Lock will become one of the five most expensive Old Masters ever sold at auction.
The top price of £49.5 million ($79 million) was reached in 2002 by Sir Peter Paul Rubens’ painting The Massacre of the Innocents.
A former Miss Spain, the Baroness is the fifth wife and widow of Swiss industrialist Baron Hans Heinrich Thyssen-Bornemisza.
The Lock was part of the huge private art collection he left behind when he died in 2002.
While most of it was sold to Spain, 250 artworks are still in the Baroness’ private collection and have been lent to the country free of charge for the past 13 years.
Announcing the sale of the John Constable painting in May, the Baroness said she needed to sell because of the current economic crisis.
“It’s very painful for me, but there was no other way out,” she told the Spanish newspaper El Pais.
“I need the money, I really need it. I have no liquidity.
“Keeping the collection here is costly to me and I get nothing in return.”
Francesca Von Habsburg, the Baroness’s stepdaughter and another museum board member, has also expressed disapproval over the sale.
“The baroness has shown absolutely no respect for my father and is simply putting her own financial needs above everything else,” she told The Mail on Sunday.
The top end of the art market has escaped many of the problems faced by the wider global economy, with new records consistently being set for individual artists.
Last month Joan Miro’s 1927 work Peinture (Etoile Bleue) sold for more than £23.5 million ($37.5 million), a record for the Spanish painter.
In May Edvard Munch’s The Scream became the most expensive art work ever sold at auction, selling for $119.9 million in New York.
Most expensive Old Master pictures sold at auction:
1. Sir Peter Paul Rubens – The Massacre of the Innocents (£49.5 million)
2. JMW Turner – Modern Rome – Campo Vaccino (£29.7 million)
3. Francesco Guardi – Venice, a View of the Rialto Bridge, Looking North, from the Fondamenta del Carbon (£26.7 million)
4. George Stubbs – Gimcrack on Newmarket Heath, with a Trainer, a Stable-Lad, and a Jockey (£22.4 million)
5. JMW Turner – Giudecca, La Donna della Salute and San Giorgio (£20.5 million)
6. Jacobo Pontormo – Portrait of a Halbadier (£22.3 million)
7. Rembrandt – Portrait of a man with arms akimbo (£20.2 million)
8. Rembrandt – Portrait of a lady aged 62 (£19.8 million)
9. Canaletto – Venice, the Grand Canal (£18.6 million)
10. Raphael – Portrait of Lorenzo de’ Medici, Duke of Urbino (£18.5 million)
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