Another top 15 Anglo investor said: “We don’t need to accept any offer. There’s no gun to our head.”

Anglo’s management has rebuffed two bids from BHP over the past few weeks.

However, the Australian mining giant is widely expected to return with a third offer next week ahead of a Takeover Panel deadline on Wednesday evening.

BHP’s most recent offer was worth £34bn, or £27.53 per share. The proposed deal involved a two-step process where Anglo’s iron ore miner, Kumba, and platinum digger, Amplats, would first be divested to Anglo shareholders before BHP takes over the rest of the business.

Anglo owns 79pc of Amplats and 70pc of Kumba, which are both listed in Johannesburg.

The complexity of the multistage process, and uncertainty around how the stakes in Amplats and Kumba would be valued post-spinout, have made investors wary.

A City fund manager who holds Anglo stock said: “BHP needs to understand how complex this deal looks to investors. They are going to end up with all sorts of bits and pieces. I would prefer BHP to do the heavy lifting and take away all of Anglo.”

Another British money manager said: “It’s difficult to arrive at what the value would be because of these pre-conditions attached. Ditching those would make things a lot easier.”

However, a third significant shareholder said the complexity was “not a priority” and they were more focused on the price BHP was offering.