England's men have lost 2-1 to New Zealand at the Glasgow National Hockey Centre.
They are now likely to have to face world champions Australia if they make it to the last four.
Both England and the Kiwis had been trying to protect 100% records from their opening two Pool B fixtures.
England can secure a top-two finish with victory over Canada in their final group game on Thursday, but Australia will then loom in Saturday's semi.
The loss to New Zealand was a first defeat for an England side that had comfortably beaten Trinidad and Tobago, and Malaysia in their opening pool fixtures.
Elsewhere on Tuesday, Wales failed in their attempt to sign off with a maiden win, losing 5-1 to South Africa.
Trinidad and Tobago won their first ever hockey game at the Commonwealth Games with a 4-1 triumph over Malaysia, while Australia beat India 4-2.