Overall, mortgage payers spend an average of 20% of their post-tax income on their housing across the duration of the mortgage (it starts at about 37% and gradually reduces over the years.
So perhaps once a family has a post-tax household income that exceeds five times the social housing rent, they could be obligated to pay the difference between their social housing rent and 20% of their household income into a fund for building more social housing? (Up to a ceiling of 90% of the equivalent commercial rent for the property)
To put some figures on this - say a family is paying a social housing rent of £1,800pcm in an area where a commercial rent for a similar property might be £3,000pcm.
So until their household income exceeds £108,000pa after tax, they aren't getting a particularly better deal than mortgage payers and they just pay the social housing rate.
If their household income goes up to £130,000pa after tax they would pay their £1,800pcm rent and be expected to contribute £367pcm towards the social housing fund to have an effective rent equivalent of £2,167pcm. Eventually if their income reaches £162,000pa after tax their effective rent equivalent rent (including contribution) would reach a ceiling of £2,700pcm which they'd be welcome to keep paying indefinitely in their secure tenancy (and it would go right back down again if their circumstances changed eg incone could suddenly crash if someone got cancer, so totally fine to stay for the security no matter what)