It will look at the costs and benefits, with a “go or no-go" decision by the end of the year.
It comes after the PM said the plan to avoid a hard border in Northern Ireland was "anti-democratic".
Business groups urged the government to act after many firms failed to get a customs number.
Office blocks are also being used to house families as 210,000 children are estimated to be homeless.
The Hong Kong consulate worker was detained for violating the law, China's foreign ministry says.