Alex Carlile, the outgoing employment spokesman, argued in vain for a more flexible approach which he believed removed the risk of pricing people out of jobs.
However, the move was immediately welcomed by John Monks, general secretary of the TUC, as a 'very important step' in the right direction. Mr Monks, treading new ground for a TUC leader by attending all the party conferences, wants a national minimum rate. He warned Liberal Democrats that their variable formula might not go down well with the party's natural supporters in the South-west and Scottish highlands and islands.
'I want to see one figure which is clear and understood, and any employer knows that if they are not paying it they are breaking the law and it is unacceptable. They cannot shift the burden of subsistence (on to the state) as so many of them are doing now,'he told a fringe meeting.
In two weeks at Blackpool, Mr Monks will be trying to counter a current of opinion in the Labour leadership that Tony Blair should water down the party's 1992 commitment to a minimum wage. One option would be to follow the Liberal Democrats' example.
The Brighton debate took place on an employment policy paper, 'Working for Change'. It offered a choice between a regionally variable minimum hourly rate, advocated by Shirley Williams, chairman of the working group which prepared the paper, and a more complex form of wage protection.
Backed by all the party's 23 MPs, the latter would enable a low pay commission to investigate any sector or firm where it believed there might be exploitation and recommend action to Parliament.
Baroness Williams told her critics to 'come up to date'. She was not suggesting a minimum set at a high level which would destroy jobs - pounds 3 an hour was the figure mooted during the debate.
'We are suggesting a modest level which at least means we are not exploiting the most disadvantaged of our people,' she said. In April last year, almost 500,000 people were paid less than pounds 3 an hour, but Baroness Williams indicated the situation may have worsened.
Since wages councils were abolished last year, the pay of almost one-third of the workers covered by them had dropped, Baroness Williams said.
Rates just prior to abolition varied between pounds 2.70 and pounds 3.20 per hour for some 2 million workers - mostly in shops, catering and textiles.
Rejecting the view that jobs would be at risk, she said that in the United States, where minimum pay was raised by 50 cents an hour in 1992, the result had been an increase in employment.
A London School of Economics study last month had concluded that Tory claims of 2 million job losses had 'no empirical foundation' and, if anything, the effect would be positive.
Sarah Ludford, an Islington councillor, said employers paying pounds 1.50 an hour were abusing desperate people. 'Millions of our citizens, including kids, live in poverty and the chief cause is low wages.'
Mr Carlile attacked the imprecision of 'something around about pounds 3' for every industry. He said there was a mass of evidence that a 'rigid and inflexible' national minimum wage would lead to an increase in unemployment.
'Shirley, I say to you: 'This is not America'. What Shirley failed to tell us about was the rampant black economy which dodges the minimum wage in many American cities.'
Supporting the minimum wage, Earl Russell, the party's social security spokesman in the House of Lords, said low payers were currently subsidised by the state.
'Every time a bad employer cuts his wage costs, the Department of Social Security picks up the bill.'
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