But despite the narrow win for the Yes camp, devolution did not go ahead.
Scots-born London Labour MP George Cunningham had successfully proposed an amendment to the legislation saying that if less than 40 per cent of the whole electorate voted in favour the plans should be abandoned.
The final result was Yes 1,230,937 and No 1,153,502.
The turnout was 62.9 per cent, but the Yes vote amounted to just 32.9 per cent of the total electorate.
Out of Scotland’s 12 regions and island areas, six voted Yes and six No.
Lothian had the closest result of, split almost 50-50 with 187,221 Yes and 186,421 No.
Central, Fife, Highland, Strathclyde and the Western Isles also went Yes, while Borders, Dumfries & Galloway, Grampian, Tayside, Orkney and Shetland all voted No.
The 1979 devolution plans did not go as far as those which eventually became reality in the Scottish Parliament.
The new Scottish Assembly would have taken charge of education, health, the environment, home affairs, legal matters and social services. It would have passed “measures” rather than “acts” but would not have had any tax powers.
There would have been a Scottish Executive headed by a First Secretary and the Assembly would have met in the Old Royal High School, which had been converted and stood ready and waiting, complete with chamber.
The Labour Government had been prompted to bring forward a devolution scheme by the steady advance of the Nationalists during the 1970s.
And although the proposals fell well short of independence, the SNP backed the creation of an Assembly as a step on the way.
George Reid, then an SNP MP and years later Presiding Officer of the Scottish Parliament, said in an interview with the Evening News at the time: “I have always thought you go as far as the Scots people want and I have always been against great loups forward.
“It is good as it stands because it allows Scots’ decisions to be taken in accordance with Scots’ priorities and we again get a forum to decide where we are going.”
The interview noted that Mr Reid believed the Assembly would be a place of “civilised legislative debate between moderate men of goodwill dedicated to Scotland’s best interests”, which might include himself and the likes of David Steel and Donald Dewar. All three were eventually leading members of the Scottish Parliament elected in 1999.
Labour’s Robin Cook, later a strong advocate of devolution, was one of the most prominent No campaigners in 1979. He claimed that with the economic difficulties which then prevailed, the devolution debate was like fiddling while Rome burned. “Increasingly, ordinary voters find the whole business totally irrelevant to the real problems which we face in the industrial and economic field.”
Regional councillor Eric Milligan, later to be Edinburgh’s Lord Provost, was another Labour politician opposed to devolution.
“An Assembly is bound to take over many of the important functions presently carried out by local government,” he declared. “This will simply lead to more and more centralisation of local govt and take decisions even further away from the people.“
He claimed 18 of the 26 Lothian regional councillors were opposed to an Assembly. But he failed in a bid to get the council to recommend a No vote after George Foulkes - then a fellow councillor, later a Lothian MSP - persuaded the council to remain neutral.
However Edinburgh District Council, as it then was, did vote 33:8 to urge people to vote No.
Margo MacDonald, later one of the best-known characters in the Scottish Parliament and at that time the SNP’s senior vice-chairman, resigned as Westminster candidate for Hamilton and said she wanted to get elected to the new Assembly instead. She said the move was an act of faith and proof of her confidence of a Yes vote in the referendum.
“The Scots must realise that the Assembly is not a plaything. It is essential for reform in Scotland.”
The cost of the devolution project inevitably featured heavily in the No campaign.
The vehemently anti-devolution West Lothian Labour MP Tam Dalyell said in a debate at the Howden Centre in Livingston: “The brutal fact is that money for paying Assembleymen, clerks, secretaries, officials, supporting staff and indeed the whole parallel civil service comes out of the same kitty as paying for the health service. Do we want more money for politicians and less money to pay hospital staff?”
But SNP MP Margaret Bain - later Margaret Ewing - rebutted claims that devolution would be too expensive. She calculated the Assembly would cost 5p per person per week - “the price of a stick of chewing gum”.
And she added: “We reckon that over £1800 million of taxpayers cash has been wasted by Westminster in the past few weeks alone. This would run the assembly at current costs for more than a century.”
Malcolm Rifkind, who had resigned from Tory front bench in 1976 over the party’s retreat from devolution, announced he would vote Yes - but said it was a “major flaw” that while Scotland and Wales were offered assemblies there was no change for England.
A letter to the Evening News complained the proposed Assembly would be “lopsided” - “dominated by Strathclyde members and loaded against the interests of those staying in the East of Scotland”.
And the Monthly Record of the Free Church of Scotland came out against devolution. “We cannot be convinced that a new public building, a new debating chamber, a new breed of politicians and a new rash of civil servants are going to make our winters one whit more bearable.”
But Stephen Maxwell, director of the SNP’s referendum campaign - argued a Yes vote was crucial for Scotland’s place in the world.
He said: “A No vote would confirm the suspicion of many foreigners, including potential investors, that Scotland is a country of loud boasts and little action.
“A Yes vote will signal to the rest of the world that Scotland is a go-ahead society with high ambitions for the future and the self-confidence to realise them.”
Towards the end of the campaign former Tory Prime Minister Lord Home announced to the Edinburgh University Conservative Association he would be voting No despite supporting devolution.
He listed “defects” with the proposals, including that the Assembly would have no power to raise revenue, it would be too large with a danger of “over-government” and it was not being elected by proportional representation.
And he argued it was better to wait for an improved scheme. “I think that more and more people are concerned to get the matter right, even if it means more time,” he said. A No vote need not imply any disloyalty to the principle of devolution, he claimed.
As referendum day loomed closer, the Evening News reported how Gordon Brown, Labour’s devolution chairman, was due to speak in support of Yes at 30 meetings over three days in a “whirlwind weekend”.
The future Prime Minister declared: “To be swayed now by the scaremongering and false fears peddled by the money men of the No campaign would be like scoring an own goal in the last few seconds of a big match.”
As it turned out the match ended in a draw and it would be almost another two decades before Scotland got its parliament.