Joe, let's look at the facts.
Based on 2009-10 rent figures (latest available from this source):
North - Median social rent is 79% of median market rents
Midlands - Median social rent is 70% of median market rents
London - Median social rent is 35% of median market rents
Rest of South - Median social rent is 78% of median market rents
Median social rents as a % of median market rents is 73% excluding London. Including London it is 66% of market rents.
Source: DCLG English Housing Survey, full household sample.
My interpretation of these results:
1. London dwellers on low income are much more heavily subsidised than the rest of the country. If all social rents were as subsidised as London (at 35% of the median market rent), then social tenants in the North would pay £28 a week in rent, in the Midlands £35 a week and the rest of the South £36 a week. Compare this to the actual median social rent average of £76 per week. Social rented housing in London is disproportionately cheap.
2. The overall average social rent is 66% of market rents (medians), or 73% excluding London. If London social rents were 73% of median market rents, they would be £177 per week, rather than the actual £85 per week. The affordable rents product at 80% would not look significantly more expensive when this is considered - only in London where the social rents are disproportionately low, does it look like a significant increase.
3. London properties will be subject to the £250-£400 per week caps. About 28,000 households will see more than £20 per week increase in costs - but the nation will save over £40m in HB.
4. If the £4m results in low income households relocating to cheaper areas, the HB cost will reduce further.
5. If the allocation of homes is prioritised for those in work, this HB cost will reduce further.