Susan Brighouse, campaigns officer at the Child Poverty Action Group, was typical: "They need to decide who they mean by the underclass; for instance, do they mean lone parents on benefit? Lone parents don't necessarily regard themselves as being outside society. If they are going to tackle social exclusion they will have to involve the people they want to help, not pronounce from on high."
One worry is that the Government has conferred respectability on a term originally popularised by right-wing American social theorist Charles Murray.
Murray used it to differentiate, Victorian style, between the deserving and the degenerate poor. The underclass, he said, describes a new sort of poverty distinguished by high rates of illegitimate births, the absence of a work ethic, crime, drugs, and a culture of dependency. People end up poor because they are innately stupid, so, he reasoned, there is little point in the state wasting money on helping them.
The term is now used more widely by politicians of all hues as a replacement for the picturesque but archaic "lumpen proletariat", but some feel it distances the very poor from the rest of humanity.
Melanie Rafe, for example, a single mother of three living on a large south London estate and training to be a probation officer, says she finds the term offensive: "It's a very demoralising word, I may come from the underclass, but I want my work to be first class. It's all part of the negative view of lone parents."
Any attempt at addressing social exclusion will involve education or "bad schools and low educational standards" as Mr Mandelson puts it, and in particular the children who leave school with nothing before disappearing off the educational map.
In his speech he promises "far-reaching changes to the educational system" and better co-ordination between agencies dealing with social and educational problems. "We are spending vast sums of money, often over and over again on the same people through different programmes, without improving their ability to participate in the economy and society."
Among those who have "dropped off the ladder of opportunity" are the 46, 000 pupils who, according to the Department for Education and Employment, left school last year with no GCSEs. Of all last year's leavers 14 per cent did not go into employment, training or further education.
Children in care have a good case for being first on the list of those in need of the new unit's help. A report published at the end of last year by the Who Cares Trust revealed that the educational prospects for children in local authority care are very much bleaker than for the rest. Between 50 and 75 per cent of these children leave school with no formal qualifications and 43 per cent had not even been entered for GCSEs.
This pattern continues as they grow older: fewer than 20 per cent go on to further education, compared with 68 per cent of the general population; 30 per cent of homeless 16 and 17-year-olds are care leavers, as are 23 per cent of the adult prison population. Care leavers are also far more likely to be unemployed.
Exclusion from school also seems to be closely linked with social exclusion. According to an investigation published last year by Dr Carl Parsons of Canterbury Christ Church College, schools are increasingly resorting to permanent expulsion as the only sanction for disruptive pupils. Dr Parsons found that 13,400 children were ejected in 1995-96, a rise of 8 per cent on the previous year.
Brian Harrison Jennings, general secretary of the Association of Educational Psychologists, said he welcomed the way the Government was tackling an employment issue through education. However, he was worried about the possible stigma attached to an "underclass" being dealt with by a social exclusion unit.
"The strongest connection linking pupils who are excluded from school is poor academic attainment. They are not dumb - anyone who can survive on the streets can't be all that stupid. But they realise that their academic attainment is poor and behave badly because they would rather be thought naughty than stupid.
"We need to obviate the necessity for such a unit by ensuring that children are equipped to learn at seven, and by providing real jobs. I think there are very few people who would willingly choose idleness. The poor have only to turn on the television to see that everything that confers status, excitement, wealth, comes from jobs."
The Child Poverty Action Group accuses the Government of timidity. "Unless there is a willingness to engage in a wider redistributive exercise, there is a risk that very poor people may gain at the expense of others a little less poor," said the group in a statement last week.
According to the CPAG, the number of people living in poverty (defined as less that half the average income after housing costs) has jumped from under one in 10 in 1979 to one in 4 in 1993-94. Nearly one in three children is affected.
Their figures also show that the gap between rich and poor has widened since 1979 - the incomes of the richest 10 per cent of the population have risen by 65 per cent compared with a fall of 13 per cent for the poorest 10 per cent.