Logic puzzle: can you solve this baffling Brexit conundrum?

At a party, the host arranges the guests in a circle and sticks a post-it note onto each of their foreheads. Each guest can see what’s written on everyone else’s post-it, but not their own.

“You are all Brexit negotiators,” says the host. “Some of you are representing the UK and some the EU, but all of you are negotiating for one or the other and there will be at least one negotiator for each side. The side you are representing is now written on your forehead. UK or EU – does anyone know which they are representing?”

Everyone shakes their head and says they don’t know.

“Does anyone know now?” asks the host.

Again, everyone shakes their head and says “I don’t know”.

But the host persists: “Now does anyone know?”

This cycle continues, to the perplexity of all and the annoyance of some. On the host’s sixth time of asking, the guests, by now wishing they’d gone elsewhere for the evening, again answer, for the sixth time, that they don’t know. But as soon as they’ve done so, some of the guests say, truthfully, “Now I know! I’m EU!”

Given the above facts, how many EU negotiators are there at the party? And what is the minimum number of guests? (Assume that all the guests have reasoned as well as they could have.)

The solution will appear here on Monday morning (UK time).