EDINBURGH (Reuters) - Scotland’s Conservatives want the fishing industry to be protected in any deal that Britain negotiates to leave the European Union after winning seats in fishing areas in last week’s national election.

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Scottish party leader Ruth Davidson made this clear at a meeting with Conservative Prime Minister Theresa May, who lost her parliamentary majority in Britain’s June 8 vote, a spokesman for the party said on Wednesday.

“Fishing is something that Ruth has talked about specifically, we are simply emphasising that this is something of huge importance to us,” a spokesman said, when asked whether fishing constituted a “red line” in Davidson’s wish list for Scotland within a new UK government.

May is under pressure from factions within her party to change her stance on Brexit, having lost her majority just as talks with the EU are due to start.

She has yet to reach a deal with Northern Ireland’s Democratic Unionist Party (DUP), which has 10 seats. And Davidson, who spearheaded the campaign to win 13 Conservative seats in Scotland, has considerable influence.

The EU’s policy allows all European boats access to EU waters and fishing grounds, which it says allows fishermen to compete fairly.

But that means that 60 percent of what would be Scottish fish is caught by other EU fishing nations, the Scottish Fisheries Federation says, arguing that the industry has been decimated by EU membership.

Both the Conservatives and the Scottish National Party (SNP) campaigned in last week’s election to withdraw from the EU’s fishing policy.

But seats in the northeast of Scotland - Moray, Gordon, Angus as well as Banff and Buchan including fishing port Peterhead - were all won by Conservatives, defeating the SNP.

Davidson has called for a “more open” Brexit and has said she wants the Conservatives to listen to other parties because voters did not give them the strong mandate May sought. She wants more emphasis on the economy over immigration in the talks, according to people in her party.

Britain as a whole voted to leave the EU in a referendum last June but most Scots wanted to stay in.

“As we leave the European Union we must leave the Common Fisheries Policy and ensure a good deal for our fishing communities,” Davidson said last week.

Scotland’s First Minister Nicola Sturgeon has told May that a new more inclusive Brexit plan is urgently needed to protect the economy and bring people together.