Joe Scarborough and Mika Brzezinski’s staff is losing its patience with the couple’s globe-trotting, raging romance.

We’re told that after a vacation in the South of France in May, which culminated in the MSNBC “Morning Joe” co-anchors’ engagement — plus numerous trips to Nantucket, Mass. — the lovebirds have taken flight once more, this time for London.

But viewers may not notice much of a difference: MSNBC has gone to considerable lengths to make it seem as if Scarborough has stayed put in the newsroom while Brzezinski appears to be on the road. But the romancing anchors’ production team has had enough.

“Joe and Mika are away together again,” huffed a show source. “ ‘Morning Joe’ is being produced as if they’re in two different locations. They are not! They are together — they are always together,” the source added.

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On recent shows, instead of sitting together at the regular table, Scarborough has appeared in front of a blue screen, similar to the ones of the NYC set, displaying the name of the show, while Brzezinski has been sitting in front of what seems to be a TV production office.

But they’re actually yards away from each other, working out of a London broadcasting facility. We’re told the pair — who secretly dated for a while before Page Six revealed their engagement in May — are in the UK on family business.

Their simultaneous absences are a headache for staff. “It’s very difficult working on a show where the two stars are in a relationship,” said a source.

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The network has shipped separate teams of producers and crew out to the UK for each host, as they work from “different locations,” we’re told … with a wink.

Meanwhile, it was confirmed on Thursday that Brzezinski has a three-book deal with Weinstein Books. Page Six broke the news of the contract, which has a worth in the high six figures. MSNBC declined to comment.