The Panelbase poll commissioned by the Scottish National Party (SNP) questioned 1,011 people in England, Wales and Northern Ireland earlier this month.
It put support for a shared currency at 71%, while 75% backed continuing the common travel area, with no passport controls between Scotland and England.
The SNP said the findings showed overwhelming support for the "common sense position".
The SNP administration's proposal is for an independent Scotland to retain sterling and create a monetary union with the rest of the UK, but opponents have questioned whether such an arrangement would be agreed, and whether it would work.
The full findings of the Panelbase poll are expected to be published in the near future, but details of two questions asked by pollsters were released by the SNP today.
The poll asked people to put aside their own views on whether Scotland should become an independent country, and questioned: "If independence does happen do you think that Scotland and the rest of the UK should continue using the pound in an agreed sterling area?"
Some 71% backed the move, while 16% said they were not sure and 12% opposed it.
A breakdown of the figures shows that 81% of Labour voters in the rest of the UK, 66% of Conservative voters and 75% of Liberal Democrat voters back a sterling area, the SNP said.
A second question in the poll stated that a common travel area has existed since the 1920s, which provides for freedom of movement throughout the area for citizens of the UK, Republic of Ireland, Channel Islands and Isle of Man. It then asked: "If independence does happen do you think that there should continue to be freedom of movement with no passport controls between England and Scotland?"
Three-quarters, or 75%, agreed, while 12% said they were not sure and another 12% disagreed.
Deputy First Minister Nicola Sturgeon said: "These are extremely welcome findings, which demonstrate that by a factor of some six to one people in the rest of the UK back the common sense position of Scotland's Government to share sterling and the common travel area after Scottish independence.
"As well as being out of touch with Scotland, it's clear that Westminster is also out of touch with people in England on these matters, across supporters of all political parties - which underlines that what UK ministers say before the referendum will be entirely different to what they do after a Yes vote.
"Sharing sterling and the common travel area is every bit as much in the interests of the rest of the UK as it is in the interests of an independent Scotland."
A spokesman for the pro-union Better Together campaign said: "The SNP have completely lost it. They are now commissioning polls to show that people in the UK value all the things that make the UK great."
The poll was conducted from December 13 to 20.