They claimed Mr Rowland's decision to criticise Mr Bock publicly would prolong the difficult search for a chairman, because potential candidates would not accept the job amid open warfare.
Alleging that Mr Bock and his advisers were behind reports last week that he cost the company pounds 5.5m a year, Mr Rowland said at the weekend that he had vetoed Mr Bock's choice of Eugene Anderson, the former Ferranti chairman. Mr Anderson did not have enough African experience, Mr Rowland said.
He added that he favoured Sir John Leahy, a non-executive director, whom he described as likely to make a 'very good chairman'. He praised him for his African experience, including an ambassadorship to Pretoria. The largest part of Lonrho's business is in Africa.
But the Bock camp claims Sir John will not take the job as long as Mr Rowland remains co-chief executive. Mr Rowland disputes this.
Sir John chairs the committee of directors charged with finding a chairman. With Mr Leclezio's contract about to run out, one proposal is that Sir John takes the senior role temporarily as a vice chairman, while the search for a non-executive replacement continues.
The two co-chief executives spent yesterday assessing the damage from the row that broke out last week over reports of a boardroom coup that failed to materialise.
Mr Rowland blamed these reports and allegations about his expenses on Mr Bock and his advisers.
The risk to the Bock camp is that the row will end up damaging the company without removing Mr Rowland. There were indications that last week's arguments have weakened Mr Bock's support among the more neutral members of the board.
However, Stephen Walls, the former Plessey chief executive brought in by Mr Bock as a non- executive director, remains a close ally of Mr Bock. He is regarded by the Rowland camp as just as determined as Mr Bock to force Mr Rowland out.
But Mr Rowland declared at the weekend he would use his wealth of pounds 220m to fight his opponents.
In the City there was disappointment that a solution to Lonrho's problems had receded still further. The shares slipped 3p to 139p. One Lonrho insider claimed: 'People are worried that Tiny isn't actually going.'