Since 2019, London has banned ads for foods that are high in fat, sugar and salt from the city’s subway trains and stations, buses and bus shelters
The British boxer posted a picture of himself wearing his belts on his Twitter feed with the words "June 20th".
Joshua, 30, regained the WBA, IBF and WBO titles with a unanimous points win over Andy Ruiz Jr in Saudi Arabia in December.
That victory saw the Briton avenge the first defeat of his professional career, in New York last June.
Joshua is set to face Bulgaria's Pulev, 38, at the new Tottenham Hotspur Stadium in north London.
Pulev, who is the mandatory challenger for Joshua's IBF title, pulled out of a scheduled meeting with the Briton in 2017 due to injury.
The prospects for a much-anticipated all-British "superfight" between Joshua and Tyson Fury suffered a setback when American Deontay Wilder said he would trigger a clause in his contract for a third meeting with Fury, the new WBC champion.
Wilder has officially exercised his right to another fight against Fury and the plan is to stage the bout on July 18 at the MGM Grand Hotel and Casino in Las Vegas, US media reported Sunday.
"We received a letter from Wilder's team on Friday night, and we agreed with the networks and the hotel that July 18 was the optimal date," promoter Bob Arum told the Los Angeles Times newspaper.
Fury stopped Wilder in the seventh round of their heavyweight title rematch in Las Vegas last week - the American's first defeat of his career - after a draw between the two boxers in 2018.
Fury's promoter Frank Warren had urged Wilder to ditch his re-match rights in return for a payment in order to pave the way for a lucrative unification bout between the self-styled "Gypsy King" and Joshua later this year.
Joshua's promoter Eddie Hearn said last week they would do "everything we can" to bring about a fight with Fury.
The 90,000-capacity Wembley Stadium could host a potential Joshua-Fury bout but it could take place overseas for financial reasons, with Saudi Arabia reported to be a potential venue.
"You go back to (Muhammad) Ali fighting (George) Foreman in Zaire when a lot of money was put up, you go back to the 'Thrilla in Manila', where money was put up. That happens in boxing," Warren told the Daily Telegraph.
"All I can say at our end is that if we can do it we'll do it, for obvious reasons," he added.
Since 2019, London has banned ads for foods that are high in fat, sugar and salt from the city’s subway trains and stations, buses and bus shelters
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