The BMA said that while it did not want to see the country shut down again, the inadequacy of recent measures suggested stricter measures were needed.
On Saturday, the UK recorded another 4,422 cases of the virus – topping 4,000 for two consecutive days for the first time since early May.
The BMA is calling on the Government to reconsider the “rule of six”, which was introduced in England on Monday, banning social gatherings of more than six people.
It wants the number of households people can visit to be reduced, arguing that the rule – under its current format – makes it possible for members of six households to meet indoors, potentially many times over the course of one day.
The association is also urging ministers to reverse their stance on getting workers back to the office. It says the public should be encouraged to work from home in order to reduce contact between people including on public transport.
The BMA said unnecessary travel and social gatherings should be discouraged.
It suggested a “take out to help out” approach – similar to the Chancellor’s Eat Out to Help Out scheme – could be introduced to reduce the number of people in restaurants.
The association also called for entrances to indoor public settings to provide inexpensive disposable surgical masks, and for people over 60 and who have underlying conditions to wear medical grade masks.
Dr Chaand Nagpaul, chairman of the BMA, said: “It is vital to reduce avoidable mixing of people at a time when the infection is spreading without the testing capacity to identify those with the infection.
“This requires revisiting the rule of six which allows members of six different household to meet indoors compared to a maximum of two previously, and reversing the encouragement to travel and return to work for those able to work remotely.
"We need to know the criteria for when different restrictions will be introduced, and local public health specialists need to have the autonomy to act in the best interests of their own towns and cities.”
Describing the country’s testing programme as “woeful”, Dr Nagpaul stressed that it has “nowhere near the capacity and agility we need to test at scale”.
He continued: “Testing is now effectively rationed and so we must prioritise testing for those who need it – such as people with symptoms and key workers including healthcare staff and teachers, along with suspected cases who are contacts of key workers.”
Cases of the virus and hospital admissions for Covid-19 are doubling every seven to eight days in the UK, according to data from the Office for National Statistics.
Meanwhile, the Government’s Scientific Advisory Group for Emergencies (Sage) said the R number – representing the number of people an infected person will pass the virus to – has risen to between 1.1 and 1.4, meaning cases could rise very quickly.
Although deaths are currently low, experts expect them to rise, with Sage saying the R number “shows that we are moving to wider spread growth in transmission at a faster rate”.
Last week, the R number was said to be between 1.0 and 1.2.
Overall, an average of 6,000 people in England per day were estimated to be newly infected with Covid-19 between September 4 and 10, almost double the 3,200 people per day from August 30 to September 5.
The figures do not include people staying in hospitals or care homes.