Both Johnson and Austin's comments come in the wake of the poisoning of a former Russian spy and his daughter in Salisbury, England, earlier this month - which Johnson said it was "overwhelmingly likely" that Putin personally ordered the nerve agent attack.
Johnson said he agreed with the assessment.
He said: "I frankly do not think England should be participating in the World Cup".
While Austin thinks that England should Boycott the games, Johnson disagreed, saying it would be harmful both to the fans - including the 24,000 fans who have applied for Visas to attend the games in Russian Federation - and the national team.
Johnson also called for Russian guarantees over the safety of England fans at the World Cup.
The UK foreign minister was then questioned as to why England's World Cup team has not been pulled from the tournament.
"The fact, that they [UK officials] categorically reject to file an official request and deliberately and arrogantly fan anti-Russian rhetoric in the public sphere bordering on hysteria, indicates that they clearly understand they have no formal pretext to go down a legal road", said Russian Foreign Minister Sergei Lavrov.
"I think it is up to the Russians to give us an undertaking that they will be safe", he said. "It is because this is a country that does have that particular set of values, that does believe in freedom and democracy and the rule of law and has time and again called out Russian Federation over its abuses of these values".
"Our country is very hospitable, and we are waiting for everyone here", Dvorkovich told the Russian News Agency TASS.
Mr. Yermakov, however, went even further this time by painting the Salisbury attack as only the latest chapter in a long-running, elaborate conspiracy against Russian Federation and its allies.
"That is what I think it was an attempt to excite amongst the Russian electorate".
Johnson said the United Kingdom authorities had been cooperating with Russians at a "policing level" but there were now questions as to how that would continue.
"I don't believe that for a minute", he said.
They remain critically ill in hospital.
"Logic suggests that there are only two possible things", Vladimir Yermakov, head of the ministry's non-proliferation and arms control department, told a meeting with foreign ambassadors based in Moscow.
The diplomat responsible for their protection is among 23 due to be expelled by Saturday.