Joseph Parker's team are ramping up the psychological pressure on Anthony Joshua by giving him an ultimatum: turn up on time for the official fight press conference tomorrow or we will start without you.

Englishman Joshua has become notorious for turning up late to press events – he kept Parker, trainer Kevin Barry and promoter David Higgins waiting for 40 minutes before their press conference in January when the fight was announced, and this latest ploy will almost certainly get under his skin because he has been boxed into a corner.

If Joshua, the IBF and WBA world heavyweight champion arrives on time for the midday (UK time) conference at Sky Television's west London studios, the New Zealanders will claim it as a victory. If he stays true to form and arrives late, it will make for an awkward scene.

"I'll tell you this – we will be in control of that press conference," Higgins told Sky TV here in London. "Whatever the start time is… AJ thinks it's fashionable to be late and or maybe he thinks he gets a psychological edge by being late. We just think it's silly and disrespectful. We will start on the dot whether Sky choose to film it or not and we will leave 30 minutes later.

Joshua v Parker: The Shorter Man Advantage. / Supplied by TAB

"If AJ doesn't show up it shows he doesn't have any respect for the media or the fans because he's been late 100 times in a row. So my first challenge for Anthony Joshua is; be on time mate for the first time in your life."

Joshua's promoter Eddie Hearn has already said he and Joshua will "goad" Higgins and Parker during the press conference, a reaction to Higgins' repeated claims that Joshua has a "glass jaw". Higgins has said he wants the Kiwi pair to repeat the claims to Joshua's face.

Hearn's admission may have already backfired, however. It has given Higgins and Parker ample time to prepare, and Higgins' latest move has turned the spotlight back on Joshua, a man who made headlines for the wrong reasons when declining to speak to the media from New Zealand and Samoa who had made the trip to Sheffield for a media day last week.

Parker, meanwhile, has been charming and accessible as usual, an attitude which has seen his stocks rise with the British media and in some cases the public. The support isn't going all one way before the world heavyweight title unification bout in Cardiff on Sunday morning NZT – some British boxing fans are hoping for a Parker upset.

Joshua v Parker: Balance and Footwork. / Supplied by TAB

"Boxing isn't just fought in the ring – there's a psychological element… I think you can see that with Joseph," Higgins said. "The confidence isn't an act, it's authentic, genuine. Joshua, he does look rattled, and this press conference tomorrow is part of that whole game.

"Everything we've done has been deliberate. Some people think we're mad – it's all a strategy, we're professionals. We will start on the dot whether Anthony is there or not. Eddie should make an effort to get his man there on time.

"I know it's a challenge, Eddie, I'm glad I'm working with Joseph Parker because he's a dream to work with."

Higgins also expressed surprise at some of the quotes attributed to Joshua in the national media here over the weekend in which the 28-year-old compared his strategy with "that of an assassin … rather than a brave warrior riding through on a horse slinging a weapon and killing everyone".

Joshua v Parker: The Reach Difference. / Supplied by TAB

Higgins said: "I'm not a mean person – I don't want to accuse him of talking gibberish, but… some of the stuff, I mean it speaks for itself, I don't want to comment.

"He looks like a man under pressure. It's all about performance under pressure, and you've got a cool, calm, collected unbeaten WBO world champion [Parker] who is genuinely relaxed and sleeping at night - and boxers can't take sleeping pills – Vada [Voluntary Anti-Doping Agency] doesn't allow it.

"I don't think Anthony will be sleeping much this week and that could be why he's saying silly things."