There are degrees of swearing which the broadcasting regulators will accept, and C$ can edit accordignly - bleeping if the more serious and unacceptbale words are used.
For a live broadcast, if Davina asks people not to swear, then Channel 4 has legally fulfilled its requirement not to allow gratuitous offensive langauge onto its airwaves unchecked. If an individual does then use a serious swearword, then the issue will be with the individual for ignoring the legal request, rather than the brodcaster for allowing the language onto its programme.