Campaigners against the controversial Aberdeen bypass have had their appeal rejected unanimously by the UK's Supreme Court.

They have been fighting plans for the 28-mile road since it was cleared by the Scottish Government three years ago and had their case heard in London earlier this year.

This latest defeat could finally allow the £400m route to go ahead. Business leaders and politicians have argued the new road is vital for the north east of Scotland's economy.

The case was brought by campaign group Road Sense in the name of spokesman William Walton.

Scottish ministers approved the 28-mile AWPR in 2009 after a four-month public inquiry, despite a raft of local objections. The scheme includes a bypass and separate fastlink road from Stonehaven.

Mr Walton argued that the fastlink had been adopted without the consultation required by the Strategic Environmental Assessment Directive (SEA), and that the scope of the public inquiry should have included the question whether the fastlink was required.

In his summary today, supreme court judge Lord Reed said that no strategic environmental assessment was needed as the scheme was classified as a project rather than a modification of a plan or programme.

He said: "The Supreme Court has unanimously concluded that the alteration of the scheme was not the modification of a plan or programme.

"The scheme which the ministers altered in 2005, so as to incorporate the fastlink, was properly classified as a project, comprising the design and construction of a road.

"When the ministers decided to add the fastlink, they altered that project, but they did not alter the framework for future development consent of projects, as a modification of a plan or programme would have done.

"Mr Walton's contention that the public inquiry held into the scheme was unfair under the common law, because its scope did not include the question whether there was a need for the fastlink, is also unanimously rejected.

"The legislation under which the inquiry was held did not require its scope to include a policy issue of that kind, and Mr Walton did not put forward any convincing argument that such a requirement arose under the common law."

The Government spent £1.1 million of taxpayers' cash defending Mr Walton's initial challenge at the Court of Session which was dismissed by Lord Tyre last August. A subsequent appeal was rejected this February.

Aberdeen City Council leader Barney Crockett said: "The AWPR will have a major and very positive effect on traffic and congestion levels in and around Aberdeen.

"It is a key piece of the region's infrastructure jigsaw which will allow better access to and movement around the city, creating an even more attractive business, leisure, retail, and tourism destination.

"We will be working closely with our partners in the scheme, Aberdeenshire Council and the Scottish Government, to move as fast as we can to get construction under way and allow easier and better access to the many exciting developments in and around the city."

Aberdeenshire Council leader Jim Gifford said: "Today marks the beginning of the delivery of the most significant piece of major infrastructure in the North East of Scotland since the discovery of oil in the North Sea in the 1960s."

However, environmental campaigners said they were disappointed. Dr Dan Barlow, head of policy at WWF Scotland, said: "Miles more expensive tarmac around Aberdeen will do little to help the ordinary citizen and will soon generate yet more traffic to fill it up.

"Scotland has already missed its first climate target, and road transport is one of the few sectors where emissions have risen since 1990. A new bypass round Aberdeen will only make this worse."

Patrick Harvie MSP, co-convener of the Scottish Greens, said: "This ruling is disappointing, but at least the judges acknowledge that the bypass is bound to have a significant impact on the environment.

"Now it seems the public purse will have to cough up a staggering £400 million for a system of roads that will simply encourage more traffic, contradicting Scotland's low carbon ambitions, and doing little to reduce congestion in Aberdeen city centre."

But Scottish Labour called for work on the bypass to begin as soon as possible. Richard Baker, the party's infrastructure spokesman and a North East MSP, said: "This decision gives the green light to the AWPR and ministers must now proceed with this project without delay.

"Any further lengthy delays to constructing the AWPR will be deeply damaging for our local economy. The SNP Government has no excuse to delay; it must look to start work on the route as soon as possible and deliver this much-needed and long-overdue improvement to our transport infrastructure."

SNP MSP Maureen Watt, who represents Aberdeen South and North Kincardine, said: "The SNP Government has stood by its commitment to build the AWPR despite the legal challenges it has faced, and today's judgment should mean that we can now move towards construction.

"When it is complete, the bypass will ease congestion in Aberdeen and improve journey times for businesses and individuals across the North East.

"It is a vital piece of missing infrastructure and the concerted efforts of a handful of protesters to derail it have frustrated thousands of people up and down the North East."