The move, agreed by European agriculture ministers in Brussels, was welcomed by the Prime Minister as "genuinely good news". It should allow the resumption of sales abroad next spring, as long as Britain passes an inspection by European experts.
However, there were warnings, including one from Nick Brown, the Agriculture Secretary, that British farmers face huge difficulties in rebuilding lost markets. Mr Blair agreed, adding: "Getting beef sales back to where they were will take time and effort."
Yesterday's meeting marked the culmination of British efforts to convince EU partners that the UK has done enough to guarantee the safety of its beef. Only Germany opposed the lifting of the ban, although France, Spain, Austria and Luxembourg abstained. The European Commission will need to rubber stamp the deal.
All sales of beef outside the UK were banned in March 1996 after Britain announced a possible link between "mad cow" disease in beef and its human equivalent, new variant Creutzfeldt-Jakob disease.
The plan approved yesterday will allow the UK to export deboned meat from animals born after 1 August 1996 and aged between six and 30 months. These could not have eaten contaminated foodstuffs.
Ministers have also received fresh scientific advice this week that the risk of BSE from beef on the bone is now "negligible". This will enable the the ban on T-bone steaks to be lifted, probably before Christmas.
However, Britain still faces several hurdles before it can start exporting meat again. In particular, EU inspectors will need to visit to ensure the terms of the agreement are being met.
Before that is done, the Government needs legislation to make compulsory a final cull of the offspring of cows with BSE to reduce fears that the disease may be transmitted from mother to calf. Of 4,756 cows identified as having been born to BSE-carrying cows, around 600 have already been slaughtered.
Yesterday, Mr Brown said that, for those reasons, he was still considering the date for the EU inspection, but he set a target of next spring.
Even then the prospects for farmers, excluded from their export markets which, in 1995 were worth around pounds 500m, are poor. In the summer Northern Ireland won the right to export under a separate scheme. Sales amount to only 20-30 tonnes a week, less than 2 per cent of the pre-BSE ban figure.
This year, Britain has confirmed 1,799 new cases of BSE, by far the largest number in the EU. Franz Fischler, the European Agriculture Commissioner, added that the inspection of conditions in the UK "is necessary to show to the other European countries that everything works well".
However, Ben Gill, president of the National Farmers' Union, described yesterday's decision as a "Christmas present" for farmers.
Cost of the ban, page 3
Leading article, Review, page 3