The UK's national galleries yesterday denied they had been "held to ransom" after it was announced Titian's master- piece Diana and Callisto had been saved for the nation in a £45 million deal.

The oil painting, one of a series of six created for King Philip II of Spain in the 16th century, was bought after a fundraising campaign involving the National Galleries of Scotland (NGS) and the National Gallery, after being put up for sale by its owner, the Duke of Sutherland.

It will be shown along with its partner, Diana and Actaeon, bought in 2009 for £50m, in London and Edinburgh, in an alternating display.

The two paintings are part of the Duke of Sutherland's Bridgewater Collection. It also contains world-famous works by Raphael that were loaned to the National Galleries of Scotland in 1945.

John Leighton, director general of the NGS, said of the second major acquisition: "From today, these great paintings belong to the British public and we could not be more thrilled that they will be available for the enjoyment, the education, and the inspiration for generations to come."

However, he denied the galleries had been "held to ransom" by the Duke, with whom he said the Galleries had a very cordial relationship.

"We could have said 'thanks for the offer but no thanks', and you can rail against the fact kings and queens and aristocrats and wealthy people have great assets we would like to have, but that's just a fact of life," Mr Leighton said.

"From our perspective at the gallery, we prefer to focus on the benefits for the buyer rather than the seller, and the benefits in terms of access to the collection, and the pleasure that they give over so many different years."

The duke could have made "double or more" the £45m price tag on the open market, the director said.

The price for Diana and Callisto was originally £50m but was reduced to £45m by the duke. The Heritage Lottery Fund gave £3m, the Art Fund gave £2m, and £25m came from the National Gallery in London's charitable reserves, principally legacies left over the past 100 years.

There was also £15m from private donations and grants from individual donors. These included around £1m from Scottish donors, as well as money from the Monument Trust, the Rothschild Foundation, the J Paul Getty Jr Trust and other sources.

There was no direct funding from Scotland, although Diana and Actaeon was bought with a grant of £17.1m from the Scottish Government and NGS funds.

Both paintings will now be displayed on a rotating basis north and south of the Border on a 60:40 ratio between London and Edinburgh.

The duke offered both paintings to the galleries in 2008 when seeking to raise money from his collections.

The £25m from the National Gallery in London "wipes out" most of its reserves, its director, Dr Nicholas Penny, said.

Mr Leighton said the Bridgewater Collection is at the heart of the NGS collections and guaranteed it was a "triple A" artistic and tourist attraction.

Mr Leighton admitted the group of 27 paintings in the Bridgewater Collection is only guaranteed to stay intact and in Edinburgh for another 18 years.

Since 1945, five works from the collection, including the two large Titian works, have been bought for the nation to secure them permanently for public view, rather than being lost to private collectors at auction.

Mr Leighton told The Herald: "The idea behind the date of 2030 is to give a sense of security for another generation."

The Scottish Government said it had already "made a major contribution towards the first picture, Diana and Actaeon ... we made it clear since 2008 that there would be no additional funds available from the Government towards the purchase of the second painting".

The Duke of Sutherland said: "I am delighted that these two great masterpieces will remain together and on view for the public in Britain.

"I congratulate the two galleries on their success in securing these works."