By Elisabeth O'Leary and Alistair Smout

EDINBURGH/LONDON (Reuters) - Support for Scottish independence has risen since British Prime Minister Theresa May came out last month in favor of Britain making a clean break with the European Union when it leaves the bloc, an opinion poll showed on Wednesday.

The poll still showed a slim majority opposed to independence, but the ruling Scottish Nationalist Party said the fact that almost half those asked said they supported secession indicated that sentiment was shifting and could embolden calls for a new vote.

In 2014, Scots voted roughly 55 percent to 45 percent to remain in the United Kingdom. But last year's Britain-wide vote to leave the EU changed the landscape because a majority of Scots backed staying in the EU.

The pro-EU SNP, the biggest party in Scotland's parliament, has said that there should be another independence vote if its views on Brexit are rejected. May has repeatedly said she sees no need for one.

A majority of those asked in the BMG survey, 51 percent, still opposed independence, the survey showed, but that number fell by three and a half points while the number supporting secession rose by the same amount, to 49 percent.

The proportions were calculated after "don't know" votes were removed in the survey of 1,067 Scottish residents, which was conducted for the Herald Scotland newspaper. Without removing the "don't knows", the proportions were 43 percent for independence vs 45 percent against. http://tmsnrt.rs/2k3fQwD

A demand for a second independence referendum from Scotland's devolved government would throw the United Kingdom into a constitutional crisis just as PM May seeks to negotiate the terms of the Brexit divorce with the EU's 27 other members.

The opinion poll findings indicate pro-independence sentiment is not yet strong enough to guarantee the success of such a vote, but the SNP said it showed Scots did not like May's plan to quit the EU's single market when it leaves the bloc.

Derek Mackay, a member of the Scottish parliament and SNP Business Convener, said if May continued pursuing what her critics call a "hard Brexit "then more and more people will see independence as the option delivering certainty and stability."

HYPOTHETICAL STILL

Michael Turner, head of polling at BMG Research said currently only 59 percent of SNP supporters wanted a referendum before Brexit negotiations were completed, which might reflect caution that any ballot arranged too hastily might be lost.

"Although support for independence has risen, in some respects, it's hypothetical still," BMG's Turner said, nevertheless adding that in statistical terms, the move in opinion was genuine.

"It is a small but significant shift towards independence."

Scotland has a population of around 5.3 million, according to the last census, slightly more than 8 percent of the United Kingdom's population as a whole. It was an independent kingdom until joining England in the Act of Union in 1707.

A report in Dundee-based newspaper the Courier on Wednesday said May believes Scottish First Minister Nicola Sturgeon could next month demand a second referendum on independence and is privately working on a strategy to deal with this.

Asked for comment, a Scottish government source said the government was still in a negotiation process with the United Kingdom which continues in good faith but it was "interesting to see that the UK government appears to accept the Scottish mandate to decide its own future, should that become necessary".

However, in his response to the report, a spokesman for May said the UK government did not believe there should be a second referendum.

Ultimately it is the United Kingdom's parliament in Westminster which takes the call on whether Scotland can hold a second referendum. Last week, a British minister told nationalists to "forget" about another vote.

While Scotland's government can present a bill in the Scottish parliament saying that a referendum will be called, such a move would be open to legal challenge.

The BMG poll found a clear majority of those Scottish residents polled - 56 percent to 44 percent - still oppose holding another independence vote before Britain finishes negotiations to leave the EU, probably in early 2019.

And while Brussels is sympathetic to Scotland's pro-EU stance, some European politicians, such as Spain's Rajoy, have ruled out membership for an independent Scotland.

Spain is sensitive over the issue due to a secessionist movement in Catalonia, where in 2014, there was an informal ballot on independence. The former head of the region this week went on trial for staging the ballot, as it was in breach of a legal order.

(Additional reporting by Kylie MacLellan and Elizabeth Piper; Editing by Guy Faulconbridge and Philippa Fletcher)