However, meeting friends and family outdoors is allowed, but only in a group of up to six people.
Weekly infection rates in Luton stand at 156 per 100,000 people while in Oxford it is 138.
"We have agreed with local leaders to move more areas into the high local Covid-19 alert level this week," Health Secretary Matt Hancock said in a statement.
"These restrictions are challenging for us all, but it is only by working together and following the rules that we will bring down the rates of infection...
"A failure to act now will only lead to longer disruption and greater economic damage," he added.
The new three-tier COVID-19 alert system set out by Prime Minister Boris Johnson came into force on October 14 across England as the country struggles to curb the spread of the coronavirus.
The alert system comprises three levels: "Medium", "High" and "Very High" with the level being decided according to local infection rates.
(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)
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