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An ongoing war of words between the UK and Welsh Governments is “not helping” the case for Scotland to stay in the UK, the First Minister has suggested.

Tweeting from his newly-established personal @AMCarwyn Twitter account – which lists him as the AM for Bridgend and directs users to the official @fmwales account for official First Minister tweets – Carwyn Jones said it was “important for Wales that our friends in Scotland stay with us”, but added the “UK Government’s behaviour towards Wales is not helping”.

He also tweeted it was “important that the Scottish referendum campaign doesn’t turn into Scottish voices saying yes and English voices saying no”.

It comes after months of cross-border conflict between the two governments over standards of public services in Labour-run Wales, which the UK coalition allege are examples of failure which would be replicated under an Ed Miliband UK Government.

Several senior UK Government figures have voiced criticism over standards, particularly in the Welsh NHS, while Welsh Labour have accused the Conservatives of waging a “war on Wales”.

The rhetoric over the NHS reached fever pitch during the Welsh Conservative Spring conference in Llangollen, when Prime Minister David Cameron said Offa’s Dyke had become “the line between life and death” and Health Secretary Jeremy Hunt said the Welsh Government was “sleepwalking into a Mid-Staffs tragedy”.

Mr Jones’ Twitter intervention comes after repeated criticism of the No vote Better Together campaign for being too negative, and echoes previous concerns he had raised about the treatment of Wales impacting on the arguments to keep Scotland as part of the Union.

He also wrote the Chancellor George Osborne last year warning that the UK Govenrment’s “dragging its feet” on giving more powers to Wales could provide ammunition for the pro-independence campaign ahead of the referendum on September 18.

But the Welsh Conservative leader, Andrew RT Davies, who is due to be campaign in Scotland ahead of the referendum, defended the Tory attacks on the Welsh Government, suggesting it was legitimate to criticise the Welsh Government’s record.

He said: “Scrutiny of Welsh Labour’s failure in policy delivery is not a criticism of the United Kingdom. It’s a criticism of Welsh Labour’s record over 15 years – something they should rightly be ashamed of.

“As a unionist party, the Conservatives are committed to defending the strengths of the United Kingdom and we will continue to promote the reasons why we are better together.”

But Mr Jones’ plea for that the campaign for a No vote be dominated by English voices came as the Defence Secretary, Philip Hammond, travelled to Glasgow to warn that a Yes vote in the referendum risked thousands of Scottish defence jobs – and warned there would be significant costs with removing the Trident nuclear capability from Clyde.

He said: “If we did have to move the Trident nuclear deterrent from Faslane as a result of the negotiations that happen after any independence vote, it would take about 10 years at least to design and construct a suitable alternative site. It would cost a very large amount of money.

“I can’t say precisely how much, but it would be many billions of pounds. And that timescale and that cost would have to be taken into account within the overall negotiations.”

The SNP said Mr Hammond was spreading “myths and misinformation” and that, in the event of a Yes vote, all existing military bases in Scotland would be retained.