Shareholders in Royal Mail’s owner and in the mining company Anglo American are awaiting a final deadline on Wednesday for firm offers that could see two of the UK’s most prominent companies fall into foreign ownership.

Czech billionaire Daniel Křetínský has made an approach to International Distributions Services (IDS), which runs Royal Mail, while Australia’s BHP is trying to buy its rival Anglo American, a stalwart of London’s FTSE 100 index.

Under UK takeover laws, companies have a limited window after making an approach to make a firm offer or walk away – known in the City as the “put up or shut up” deadline. For both businesses the cutoff point is 29 May.

Of the two, the bid for Royal Mail’s owner by Křetínský’s EP Group, which made its money in coal-fired power stations, appears more likely to succeed. IDS said earlier this month that it was “minded to recommend” the proposal, if a firm offer was made after talks.

Křetínský’s bid values the postal service at £3.5bn, although that is still well short of the £5.3bn market value the company reached in late 2021. IDS shares were trading at 324.6p on Tuesday morning, well below the 370p a share offer from EP Group. Shares generally trade below an offer price if enough investors believe there is a significant chance the deal will fall through.

On Friday, the IDS board warned in delayed annual results that Křetínský’s bid could create risk around the company’s finances beyond the coming 12 months if the new owners were to struggle to maintain existing loans and secure fresh funding.

If Křetínský does make a firm offer, a takeover of the 508-year-old postal service by a foreign firm would face significant political scrutiny. The chancellor, Jeremy Hunt, has said the government would examine the national security implications, and it is likely that whoever wins the 4 July general election would continue that policy.

BHP’s attempt to take over Anglo American has so far been more troublesome. Anglo has rejected three takeover offers, the last of which was worth £38.6bn. BHP has raised its offer from an initial £31bn, and some analysts believe there is limited scope to increase the bid, which would already be the largest in the history of the mining sector.

A combined company would be a global player in markets for commodities including iron ore, potash, and metallurgical coal used for steelmaking. Anglo American’s copper assets are also thought to be particularly attractive to BHP, because of the metal’s crucial role in the transition to a net zero energy system.

Anglo’s chief executive, Duncan Wanblad, has responded to the bid with a strategy to overhaul the 107-year-old company, including a pledge to break up the business and sell its platinum division and its De Beers diamond arm.

The bids have attracted particular scrutiny because some analysts are concerned that British businesses are fundamentally undervalued when compared with rivals in other countries. Stuart Clark, the portfolio manager at Quilter Investors, said last week that investors should beware the “comforting short-term boost to investors’ portfolio” from increased mergers and acquisitions (M&A) activity.

“Instead, there needs to be a renewed focus on improving the competitive landscape for UK business and the UK stock market,” he said. “This, combined with an upturn in economic activity, will do far more to investor returns than the sugar rush of acquisitions.”

The deadlines could be extended by the Takeover Panel, the UK’s independent regulator of M&A activity, if the target companies want more time to talk through a deal. Anglo American has already extended its deadline for talks by a week, reportedly after investor pressure to enter negotiations.