Leeds City Council has asked the Government to ban households in the city from mixing.
Concerned council leaders want the new measure to be brought in to help limit the spread of coronavirus.
It comes as the city has seen soaring infection rates and new cases that have seen it placed on the Government's "areas of concern" list.
In a letter seen by the BBC, the council asked ministers to implement the measure and for changes to care home rules and test and trace.
However, officials have asked that meetings of six still be allowed in gardens.
In the letter sent to the government Leeds City Council is said to have asked for a ban on households mixing indoors and an easing on care home visits to one family member.
It also wants the local authority to gain control of one in five Covid-19 tests through Test and Trace to allow for faster local contact tracing.
The authority's final requests include supermarket priority hours for those who have been shielding and a scheme so secondary school pupils have access to a smartphone with the NHS Covid-19 contact tracing app.
It is not yet known if the government have responded to any of these requests.
A similar request to place a 10pm curfew on pubs and restaurants in the city earlier in September was previously rejected by the government.
This was before the national guidance came into effect today.
