James Murdoch has narrowly survived a rebellion by independent Sky shareholders to be re-elected as chair of the British satellite broadcaster.

Just 51.6% backed Murdoch to stay in the top job. Concern among the dissenters centres around what they see as a potential conflict of interest, given his role as chief executive of 21st Century Fox, which is trying to buy Sky in an £11.7bn deal.

Only 36% of independent investors , however, supported the company’s remuneration report. The total pay package for Sky’s chief executive, Jeremy Darroch, quadrupled to more than £16m in the year to the end of June, despite a hefty fall in annual profits at the broadcaster’s UK and Ireland business. About £12m of this came from a one-off payment from a long-term incentive scheme, but he also received an annual bonus of £1.9m.

The City investment group Royal London said Murdoch’s role as chair was inappropriate and that the company needed a “truly independent” chair. It also said executive pay at Sky was too complex and that bosses could receive huge payouts if the Fox deal went through.

Three major shareholder advisory groups – Institutional Shareholder Services, Glass Lewis and Pirc – had also urged investors to oppose executive pay at the group and Murdoch’s re-election.

Despite their position, Murdoch’s level of support actually increased from 47% last year, and the votes attached to Fox’s 39% shareholding in Sky meant that both his reappointment and the remuneration report were approved comfortably overall.

Fox’s bid for the 61% of Sky that it does not already own is being investigated by the Competition and Markets Authority on the basis of media plurality and broadcasting standards. The culture secretary, Karen Bradley, announced last month that she was referring the deal to the CMA after a review by the media regulator, Ofcom, created “sufficient uncertainty” about the deal.

Murdoch said at the Sky annual meeting that the companies were “engaged constructively with the regulatory authorities” about the deal. He refused, however, to answer questions from investors about whether Sky’s reputation could be insulated from the sexual harassment scandal at Fox News, which led to the departure of its chair, Roger Ailes, and anchor Bill O’Reilly. He also refused to comment on whether Fox was getting a “sweetheart deal” on the price it would pay for Sky.

One shareholder, who did not give his name, said to Murdoch: “I have the same problem with my dad. Even though I wasn’t talented, he put me in charge.”

In response to the question about the Fox News scandal, Darroch said the “whole board are incredibly supportive and behind Sky” and that it wanted to make a “broader contribution” to society.

Martin Gilbert, the deputy chair, said the board had looked at the Fox takeover in the best interests of shareholders and had had “impartial discussions” that did not include Murdoch or other Sky directors with connections to Fox.

Gilbert added: “I am not going to comment on the 21st Century Fox issues because this is the AGM of Sky, but I am pretty confident that it will not have an effect on the CMA’s investigation.”