Chris Weston, chief market strategist at spread betting provider IG, said the polls had increased investors' risk sentiment, but warned that markets were still fragile and could easily turn negative.
"The remain camp has polled well in a weekend Survation poll (for the Sunday Mail). The odds of the U.K. leaving the EU have fallen below 30 percent again, but there are at least five more polls to go," he said in a note published early Monday morning.
"For now though risk appetite has increased with a 1.3 percent increase in GBP/JPY this morning, S&P futures have rallied 0.6 percent, oil is up 0.7 percent and gold 0.9 percent lower."
This recent shift in public opinion from leave to remain is an important indicator of how the country might vote in Thursday's referendum.
"In referenda, what normally happens is in the last few days there is a swing back to the status quo," James Morris, partner and director of the European office at Greenberg Quinlan Rosner, told CNBC Monday.
"Over the weekend, there's been two or three polls that have shown a shift back towards the remain side from a leave win."
However, polling data has come under greater scrutiny this year, after polls failed to predict the results of the U.K. general election in 2015. This has led some to question the value of opinion polls.
"Obviously, there are some limitations to opinion polls. Even though polls based on true random probability samples are the best known method of prediction, the error margins are often larger than we would expect mathematically," said Rainer Schnell, director of the center for comparative social surveys at City University and Kathrin Thomas, a research associate at the center, in a joint statement emailed to CNBC.