The Paying Names Action Group wrote to all 16 Lloyd's council members this week, seeking a "magnanimous" gesture for the market's most loyal members.
The paying names are members who paid all their debts on time but have been treated worse in the rescue plan than others who dug in their heels and refused to pay.
Mr Rowland dashed the hopes of the paying names, saying: "I'm afraid the offer is exactly the same for them as for everybody else ... There are no possibilities of changes. The offer is as it is."
Tony Welford, chairman of the paying names action group, said: "We are very very sad. Several thousand of us paid up and as a result of our honesty we are ruined. They reward the people who don't pay and punish the people who do, turning morality on its head."
With unfortunate timing, Mr Welford's clearing bank contacted him yesterday demanding he sell his house to cover bank guarantees.
Mr Welford said: "Lloyd's has given assurances that names will not lose the houses they are living in but the bank is not prepared to believe that assurance." He added: " I will be absolutely bust and relying on the DSS."
Mr Rowland's statementfollowed an overwhelming vote by 34,000 Lloyd's names this week in favour of the pounds 3.2bn rescue, with 91 per cent accepting - though the offer is open until 11 September in the hope of reaching the "high nineties". Lloyd's council confirmed that the offer had gone unconditional, and now awaits governnment approval.
In the UK, 94.7 per cent of the 26,500 names backed the plan, while the US proportion was 69.2 per cent. More than 99 per cent of those names continuing to underwrite at Lloyd's accepted.
About 800 US names appear to be holding out as well as more than 1,350 in the UK, though some may change their minds by the final closing date.
With Lloyd's planning to take action against the refuseniks to recover debts and some American names trying to reopen a legal action that was blocked by an appeal court earlier this week, the rows are expected to rumble on for years.
Lloyd's confirmed that the deposits of US names who have refused to join the rescue will be drawn down.Reuse content