The official BBC title of the British television programme is Dragons' Den, with the apostrophe after the s.
The plural possessive title refers to the den belonging to multiple dragons, the programme's panel of investors. British branding and the programme's Wikipedia title use “Dragons' Den,” although informal writing frequently uses the singular “Dragon's Den.”
The distinction matters because the British series has several dragons rather than one. The panel has changed repeatedly since the programme began, with investors such as Peter Jones, Duncan Bannatyne, Deborah Meaden and Theo Paphitis appearing in different periods.
The title is also easy to confuse with other national versions. Some adaptations use names such as Shark Tank, while the British programme retains the Dragons' Den branding. The question asks for the official British title, not a common informal spelling.