The Murdoch family are under mounting pressure to increase their takeover bid for Sky in the wake of the pay-TV giant's successful Premier League rights auction.

Sky retained its status as the dominant Premier League broadcaster and slashed its annual bill by nearly £200 million ($380m), prompting renewed calls for a more generous offer from 21st Century Fox.

Investors rushed to buy Sky shares in the hope of making a quick profit if the deal for the 61 per cent of the company not controlled by the Murdoch family is completed.

Heavy trading drove the price up 2 per cent to £10.82, above the £10.75 offer, as confidence increased that Fox will be forced to improve its bid.

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Analysts said that the value of Sky had been boosted by £2 per share by lower football costs.

The Premier League's failure to attract new money from US tech giants punctured City predictions that Sky's bill would increase as much as 45 per cent, on top of painful 83 per cent inflation at the prior auction three years ago.

Sky shareholders are preparing to face down Fox when the deal is put to a shareholder vote - potentially in early summer if Fox strikes a deal with competition watchdogs on the independence of Sky News.

Fox is pursuing a scheme of arrangement, a method of takeover that seeks the backing of the courts.

Compared with a simple takeover offer it has a higher threshold for approval but makes it easier to force out opponents.Under a scheme of arrangement, only around 15 per cent of shareholders could block Fox's bid. Under a simple takeover offer, meanwhile, half of the independent shareholders, more than 30 per cent of the total, would be required to stop Fox gaining control.

However, a band of just 6 per cent could cause trouble by -refusing to sell.

Sky cautioned investors that lower Premier League costs do not necessarily mean higher profits as the cash will be redeployed in other battles such as tackling the threat from Netflix in big-budget drama.

Nevertheless, the company's strengthened finances mean its independent directors, led by deputy chairman Martin Gilbert, will be under pressure to renegotiate forcefully with Fox.

Aggressive hedge funds, including specialists in making fast money on takeovers such as Paul Singer's Elliott Management, have built up sizeable stakes in Sky.

Some hedge fund managers, including Rupert Murdoch's former son-in-law Crispin Odey, have already made repeated public demands for a price bump.

The deal hinges on what proportion of Sky shareholders are ready to vote against a scheme of arrangement at £10.75 per share.

The scale of the challenge faced by Fox is currently impossible to judge from public disclosures as many shares are held via banks with the true owners concealed.More traditional City institutions could back the hedge funds too.

When Fox's bid was first revealed in December 2016, Standard Life joined calls for a more generous price, saying £10.75 should be a "starting bid" only.

The investor has since merged with Aberdeen Asset Management, a deal that made Gilbert its joint chief -executive.

Standard Life Aberdeen declined to comment on the Sky takeover.

Sky and Fox also declined to comment.

- This article was first published by the Daily Telegraph