On Friday Mr Rowland wrote directly to individual Names, urging them to accept the offer rather than risk long and expensive litigation.
This was 'a much fairer and quicker solution than would emerge if we let events take their course'.
But this was dismissed by the rebel action groups as an attempt to split opposition to Mr Rowland by appealing over their heads to the rank and file.
The offer, which is open until 14 February, is designed to wipe the slate clean on the torrent of legal claims by Names against the managers of underwriting syndicates. The once- for-all payment would then leave the way clear for Lloyd's to resume on an even footing, but a majority of Names are understood to have rejected the scheme already.