The UK Foreign Office could not confirm whether the two cases were related, nor when the Britons were arrested.
At least some of those being held are from an global language school, Education First.
The police statement did not identify the foreigners.
On its travel advice website, the United Kingdom government warns of "extremely severe penalties for drugs offences in China, including the death penalty".
Four Britons have been arrested in China, the British embassy said, two days after Chinese police announced a drug bust there involving 16 foreigners.
Foreigners under administrative detention could spend up to 15 days in jail, and be deported from China after that period; however, being in administrative detention doesn't block future criminal charges.
However, when asked if all foreign teachers at the school are approved by the government and have been issued with a valid work license, a spokesperson at the institution said they had no information in this regard.
China's state radio said some of the detained individuals were teachers at an English education centre operated by EF Education First, a privately held Swiss firm that operates in 114 countries.
The embassy did not comment on the circumstances leading to the arrests in Jiangsu province.
The company also noted that it has a "zero tolerance" policy regarding drugs, that it "absolutely forbid" to consume or possess illegal medication or drugs, and anyone found in violation would see their employment contracts terminated. The alleged offences "were limited to seven of our teachers and did not take place during working hours or impact any students".
According to a spokesperson from EF Education First, the four centers in Xuzhou EF Youth English are now operating as usual and students' learning or curriculum had not been affected.