Parker had his picture taken with Haye and fellow Englishman Joyce, 32, a silver medallist at the 2016 Olympics, and the New Zealander's weight loss after a tough training camp and diet is clear to see.
The 26-year-old, dubbed the "King of Pies" by talkshow host Graham Norton, looks extremely lean for his big challenge against Joshua at Cardiff's Principality Stadium on April 1 NZT.
Trainer Barry said on arrival in London that Parker would have a good week of training before tapering off next week.
"We're going to be in the gym in about two hours' time today for about an hour and a half getting a good sweat up," Barry told Sky Sports UK.
"We'll hit the ground running on Monday. The first week back here will be a good solid week for us before a tapering off phase. Next week will be about staying mentally and physically sharp.
"We've had a great camp, Joe is in a good mind-space at the moment. I'm very happy with what he's showing me. We come here with a lot of confidence."
Parker said: "I'm young, fast, strong, my movement is good. I have a great team behind me, I have a nation behind me – two nations – and I'm going to represent, so that's what I have."
Haye, who has loaned his London gym to Parker while he is in the city, is preparing for his re-match against Tony Bellew on May 5.
The fight was originally to be held in December but was postponed due to Haye suffering a biceps injury. Haye lost the first fight by a dramatic stoppage during which he was hindered by an Achilles injury and said his tactics were all wrong after Bellew got under his skin.
Parker, asked if there was a lesson there for him, said: "I just have to listen to my team, follow my plan, execute it well, and then come out with the victory."