An increase in Covid-19 cases has sparked fears that the Midlands city could see stricter measures imposed to contain the spread of the virus.
According to the latest available data, Birmingham’s infection rate was 30 people per 100,000 for the seven days leading up to 16 August.
This is up from 22.4 for the week before then.
Dr Jones told Good Morning Britain viewers transmission is “rising” in Birmingham.
“If that trend continues, I think it would be inevitable that the town would have to go into lockdown,” the GP said.
He added: “What happens in the next week is really important”.
Dr Jones said social distancing needs to be “really closely adhered to” and social gatherings must not happen in large groups.
“It really is important, that will keep the transmission from rising further,” he added.
Officials have warned that Birmingham is “at a knife edge moment” and risks new measures over the level of coronavirus in the area.
The leader of Birmingham City Council has said the city will be “forced to go back to the dark days of spring” if more is not done to contain Covid-19’s spread.
Elsewhere in England, Oldham’s council leader has also warned of a “very real threat” of a local lockdown being imposed on the area.
Sean Fielding said a local lockdown, which has not been ruled out by the UK health secretary, was being considered by the government.
Several areas in England have seen tightened restrictions amid a surge in local cases.
Parts of the north-west – including Greater Manchester and parts of West Yorkshire – have faced a new ban over household mixing, with residents prevented from going over to other people’s homes or gardens.
Leicester saw some of its lockdown measures eased earlier this week, after the city had been held back from relaxing restrictions as the rest of the country opened up due to local coronavirus cases.
Additional reporting by Press Association
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