Mr English's comments came after 16 arrests last week in Cromwell, Queenstown and Glenorchy as a result of Operation Dove, which targeted LSD, BZP and ecstasy suppliers in the area.
Of the 16, nine have appeared in either the Queenstown or Invercargill district courts.
The remaining people are due to appear in the Alexandra District Court on July 1.
Last week, Queenstown Lakes Mayor Clive Geddes told the Otago Daily Times he had seen nothing to indicate drugs were more of an issue in the area now than in the past.
Mr English said in a statement the arrests were worrying, and he hoped they were not a sign drug problems were becoming "entrenched" in Queenstown.
"Unfortunately, the atmosphere of adventure and fun that attracts people to visit Queenstown may also be responsible for encouraging the worst kind of element into the area.
"We do not want to see the danger and the dysfunction associated with hard drugs becoming part of the culture in Queenstown.
"And whether these latest arrests are a sign of a growing drug culture, or merely a reflection of a problem that already exists in the town, it must be cause for concern.
"Police have already admitted that drug dealers from around the country and overseas head to Queenstown during the ski season to ply their wares. This, coupled with the fact that Queenstown has a reputation as New Zealand's party town, creates an environment where lawlessness can flourish."
Last week, Detective Sergeant Grahme Bartlett said police were aware of people - some who lived in Invercargill, Dunedin and Christchurch - who made a full or part-time living from the sale of drugs in Queenstown, particularly in winter.
Mr English commended Queenstown police on their efforts to date, and said they had "a big and important job ahead of them". Det Sgt Bartlett declined to comment further on Operation Dove, or on Mr English's statement, when contacted.
