On Monday you quoted a Department of Work and Pensions' spokesman saying housing benefit is "unfair because some families on benefits had been able to live in homes that most working families not on benefits could not afford" (Poor priced out of 800,000 more homes, 2 January). On Tuesday Liam Byrne wrote that Beveridge "would have been horrified at the long-term unemployment breaking out all over Britain ... and appalled at the spiralling cost of benefits" (Beveridge for this century, 3 January). Neither quite says that housing benefit is only available to the workless, but both strongly give that impression.

Housing benefit is designed to redress imbalances between income and rents, whatever a claimant's source of income. Only a minority of claimants are unemployed – most are in work, retired or disabled. For these groups, the housing benefit bill is driven by low wages, high rents and the level of other state benefits – not by the "idleness" which Beveridge rightly aimed to slay. It's no surprise that the government, wishing to exacerbate resentment between the working and non-working poor, likes to pretend that housing benefit is only for the unemployed. Labour should take care not to sustain the same myth.
David Griffiths
Huddersfield, West Yorkshire

• Liam Byrne blames the large benefits bill on a "something for nothing" attitude by some of the poor, which skews behaviour away from hard work and saving. Both assumptions are false. Research by Peter Taylor-Gooby, Hartley Dean and others has shown that the vast majority of those on benefits and able to work are desperate to do so. Second, the steep rise in the benefits bill in the last 20 years has been due to an increasing number of people on very low wages and pensions, and the disappearance of affordable housing. The £20bn a year spending on housing benefit would indeed have appalled Beveridge, as Byrne says; but it has grown exactly in line with real increases in rents, especially in the private rented sector, and the decline in supply of affordable housing. This is due to the abject failure of governments since the 1970s, including New Labour, to develop a serious housing strategy.

Similarly, tax credits were introduced by New Labour to deal with stagnating or falling real wages for the working class; the minimum wage was set far too low. The irony of the large benefits bill is that, far from featherbedding the feckless poor, housing benefit goes straight into the pockets of landlords, while tax credits enable employers to pay below a living wage and thus subsidise their profits. 
Dr Jamie Gough
Co-author, Spaces of Social Exclusion, University of Sheffield

• Liam Byrne would do well to remember not only the principles on which Beveridge's social security proposals were premised, but his assumptions. Beveridge assumed a post-war government would sustain full employment, ensure an adequate supply of affordable housing and that national insurance benefit levels would be set at a level sufficient to meet the cost of such housing. None of these assumptions were fulfilled. Any government seeking to honour Beveridge's principles would have first to ensure the availability of decent jobs and affordable housing for all, before reforming the social security system.
Professor Hartley Dean
Department of social policy, LSE

• Liam Byrne told the Labour conference less than four months ago that in his constituency there were about 30 people chasing each job vacancy. Will he now reassure all the 29 unsuccessful job-seekers that they will not be personally blamed or penalised for the shocking levels of unemployment? Will he also make it clear that any reduction in the cost of housing benefit must be at the expense of the private landlords who are milking the system, not of unfortunate tenants who are merely asking to be allowed to remain in the homes and communities where they live?
Francis Prideaux
London