Spire Healthcare, the private hospitals operator, is facing calls from leading investors to put itself up for sale.
Sky News has learnt that shareholders including Achilles, an activist investment trust co-founded by the prominent City fund manager Christopher Mills, wants Spire to explore talks with potential bidders.
City sources said that Achilles and other Harwood Capital Management entities, which hold roughly 5% of Spire's shares, were among a number of investors who believed the company was significantly undervalued.
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Spire runs 38 hospitals and more than 50 clinics, medical centres and consulting rooms across the UK.
It is the largest provider of hip and knee operations in the country.
Run by Justin Ash, chief executive, the company is chaired by the City grandee Sir Ian Cheshire.
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Achilles, which is managed by Robert Naylor, is understood to have communicated its wish for the company to hire advisers to run a formal sale process.
Spire has a market capitalisation of close to £820m, although its real estate assets alone have been valued at more than £1.4bn.
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The company has told investors that it was committed to delivering value for shareholders
"The Board will continue to actively evaluate and implement any appropriate action that drives long term shareholder value," it said alongside results in July.
It was unclear on Wednesday whether any formal approaches had been received by Spire's board.
Achilles declined to comment, while Spire has been contacted for comment.