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The Swedish group's performance of Waterloo at the event held at Brighton Dome in 1974 went down a storm, but the UK panel didn't award them any points.
The UK entrant that year was Olivia Newton-John, said to have been a favourite at the time with the track Long Live Love.
Speaking on BBC Breakfast, Ulvaeus suggested it could have been their plan to give Abba no points as their biggest possible threat to another UK victory.
"It certainly could have been," he told entertainment correspondent Colin Paterson. "Because the Brits were the first ones to embrace us after winning, so the jury could have been as cunning as that - [it's] very likely actually.
"Because it's kind of strange they would give us zero points. It sounds like they were trying to do something cunning."
The songwriter said his bandmate Anni-Frid Lyngstad is a friend of Newton-John's and had spoken with Australian star, who came in fourth place, about it.
"Frida is a good friend with Olivia. She says that Olivia knew that we would win," he said.
The Eurovision win allowed the group to flourish and propelled them toward superstardom
This year's postponed Eurovision Song Contest will see Sweden compete in the first semi-final with their entrant Tusse.
As one of the Big Five countries the UK's entrant, James Newman, will definitely compete in the final.
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