So, as mentioned in this post, the first of many, a well-known and highly-paid BBC presenter has, according to reports coming from The Sun (a British muck-racing tabloid with zero morals or conscience, which may or may not be relevant), been paying tens of thousands of pounds to a teenager for nude pictures. The kid then spent it on drugs.
As this... "arrangement" went back to when the teenager was 17, if nude photos were sent before their 18th birthday then it would count as a sex offence (at least according to commentary I've read from.other news sources: you can have sex at 16 but you can't send nude photos until you are 18). "Nonce" is British slang for a sex offender.
Various presenters have been scrambling to say it wasn't them as they are in work on Monday but the joke suggests anyone not gainfully employed by the BBC this week might be a bit nervous.