Westminster council is thought to be planning to adopt a similar policy and planning a higher cap of £50,000 or £60,000, while authorities outside the capital are expected to set lower ceilings to reflect lower salaries.
The proposals come after new laws came into force last month, spelling an end to the "tenancy for life" and giving councils more flexibility on dealing with waiting lists.
While they do not set any salary cap, housing minister Grants Shapps has suggested that those earning more than £100,000 should not be entitled to a council home.
The new laws also suggest that councils should set fixed-term tenancies for all new tenants, generally for five years, and mean that in future no one will be able to inherit a council home.
Andrew Johnson, head of housing at Hammersmith and Fulham, said that under its plans, the proposed five-year tenancy for residents would be reduced to two years if there was evidence of rent arrears or anti-social behaviour.
He said half the annual council house allocation each year would go to people in jobs or training or special priority groups. Currently, the authority gives just 15% of its homes to those in work.
Mr Johnson told The Times: "We want to incentivise residents to make the most of their lives. Council housing can be a great safety net to help people get back on their feet - but it should be a springboard not a destination.
"The current system does not promote personal aspiration or provide tenants with any incentive to try to move into home ownership and does not make the best use of the housing we have."