Southampton City Council, which holds one of the finest art collections outside London, is planning to sell precious artifacts to help fund a museum dedicated to the Titanic.

Sir Alfred Munnings' renowned 1937 work After the Race – valued at around £4m – as well as Eve by the French sculptor Auguste Rodin, which is worth about £1.5m, are to be auctioned off for the museum which will include a walk-around replica of the doomed, Belfast-built ocean liner.

The plan has caused consternation in the art world, where strict rules apply over the sale of publicly owned works of art.

Critics fear that if the Museums, Libraries and Archives Council (MLA), which polices Britain's public galleries, allows the sale it will set a precedent for local authorities up and down the country to ransack their collections.

There is also disbelief that the work – Munnings is considered one of the greatest painters of horses – will be sold to pay for a themed visitor attraction. Some critics argue that, as the Titanic sailed from Southampton only once, the city has a tenuous connection with the ship which was built in Belfast.

The plans are the first big test of the MLA's tough new guidelines on art sales, drawn up after Bury Council sold a Lowry for £1.4m in 2006 to plug a budget gap. The row could also embarrass the Heritage Lottery Fund – which is stumping up £5m of the £15m cost of the Sea City Museum.

“The Museums Association guidelines require that any sale of work should benefit the collection. There are no indications of this happening,” chief executive of the Royal Academy of Arts, Charles Saumarez Smith told The Independent on Sunday. “Instead, the funds are being used as matching funding for a maritime museum.

“I don't think HLF should be funding a new heritage attraction which requires sales of major heritage assets.”

The HLF is understood to be aghast at the plans, however. A source said that the HLF would take a “dim view” if the painting was sold, and any sale could “put at risk” the £5m grant.

Councillor John Hannides, Southampton's leisure chief, argued, however, that the money will be used to enhance the collection.

“Building the museum will effectively provide a new wing for the gallery,” he said.

“I have made a presentation to the MLA's board, which is chaired by former poet laureate Andrew Motion. At the moment we can only display 250 of our 3,500 works at any one time. The new wing will allow us to display a further 100 works. The Sea City Museum will attract hundreds of thousands of visitors to Southampton.”

A campaign – Save Our Collection – has been launched on the south coast to try to prevent the sale.

“The City Art Gallery is one of the most distinguished collections in the country and, where 20th-century British art is concerned, arguably the best outside London and thus one of the best in the world.

“What it lacks is sufficient support from the council and citizens of Southampton,” said Edward Chaney, professor of fine arts at Southampton Solent University.

The art critic Brian Sewell added that although Munnings is currently unfashionable, that is a stronger reason not to sell.

“When you sell an unfashionable painting, the problem is you cannot buy it again when it becomes fashionable,” he said.

“If you have a good Munnings, which they have, even if it's out of fashion, that's even more of a reason for hanging on to it.”