This morning I was interviewed on LBC radio responding to comments by the Shadow Work and Pensions Secretary Rachel Reeves about the spare room subsidy cut.

She made the familiar but false claims about how there were no families in overcrowded housing willing to swap with those with spare rooms and that no help was available to the disabled.

Miss Reeves is the MP for Leeds West. Last week Leeds Council told me, via an FOI request, that 8,939 households were affected by the spare room subsidy when it was introduced – that is now down to 7,043. A fall of over 20 per cent. The Government’s estimate of saving half a billion a year may now allowance for the impact of work being more rewarding. It is commons sense that those wishing to avoid downsizing but faced with paying £15 or £20 towards their rent will consider work worthwhile – which it wasn’t before.

Then we could consider Doncaster – which includes the constituency of the Labour leader Ed Miliband. On January 16th Doncaster Council told me that “of the 3876 tenants affected at 01/04/2013, 1008 aren’t affected today.” That’s a fall of more than a quarter.

Many more will still be in Housing Benefit in part time work but have increased their hours to pay the extra.

In Leeds West and Doncaster North – as in the rest of the country – this policy is giving a spur to get off benefits and into work. It is alternatively prompting people with spare rooms to swap with those in desperate overcrowding.