Renters who give up their council or housing association homes to move to a smaller property are being offered at least £1,000 in an effort to get more families off the waiting list.
Greenwich Council had previously offered £350 per bedroom for tenants who wanted to downsize, but for the next year the incentive is being nearly tripled, and will now be offered to housing association tenants too.
The council will also pay removal costs, while on top of the £1,000-per-bedroom incentive, tenants who can arrange a mutual exchange will get an extra £500.
Households taking part in the scheme will also be bumped up the waiting list, enabling them to find a new home sooner.
It is the first time Greenwich has increased the money on offer to downsize in 20 years, with just a handful of households taking up the offer in recent years.
Officials hope the scheme will not only bring down the waiting list but bring down the huge bill for temporary accommodation, which is costing £72 per night on average for each family in a hotel room.
When the scheme was approved in March, councillors were told that more than 40 per cent of homes vacated by “under-occupiers” were expected to be taken by people currently in temporary accommodation.
Older tenants who want to downsize will be eligible for a room for themselves plus one extra bedroom if they are on pension credit and exempt from the bedroom tax, meaning they can still have carers come to stay.
A council spokesperson said: “Our new package of financial incentives will be available to under-occupying residents who want to downsize to a smaller home and help many families in overcrowded conditions move to a safe and secure home that meets their needs.
“If you know of anyone, including under-occupying tenants in housing association homes, who could benefit from this scheme then please ask them to get in touch with us.”

Greenwich has more than 27,000 households on its housing waiting list, one of the highest totals in London.
However, more than 20,000 of those households are in the lowest priority band and are unlikely to be given a home.
Two years ago Pat Slattery, the cabinet member for housing, suggested those low-priority cases could be taken off the list – as they have been in other boroughs – and plans to address this are expected soon.
More details about incentives for downsizing tenants are on the Greenwich Council website.
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