The Food Standards Agency has found only 29 samples of beef products contained levels of horse meat 'above 1%' after testing 2501 samples following the contamination scandal, in results described by the industry as "encouraging".
Although 950 tests are still in progress, almost 99% of beef products did not contain horse DNA above the level of 1%.
The 29 products that did contain horse meat all related to products that have already been reported and all of them tested negative for vet drug phenylbutazone, known as bute, which can pose a health hazard to humans.
The products linked to the positive results were confirmed to be Aldi's special frozen beef lasagne and special frozen spaghetti bolognese, the Co-op's frozen quarter pounder burgers, Findus beef lasagne, Rangeland's catering burger products, and Tesco value frozen burgers and value spaghetti bolognese.
FSA director of communications Stephen Humphreys said he could "assure" the public that all seven had now been taken off the shelves.
But it would likely be "impossible" to ever know the full extent of horse meat mis-labelling, FSA director in Wales, Steve Wearne, said.
He said: "What we have in these set of results is a snapshot of what has been on the market and provided by wholesalers, by caterers, by retailers in the period between January, when this story broke, and now.
"We don't have any reliable information on what might have gone on before January 15."
FSA Chief Exec Catherine Brown said: ‘Since this incident began on 16 January, businesses have been carrying out a large number of tests. We said that industry should share those results with us, and the public, and we asked for the first results to be with us today.
‘More important for consumers, it shows that in the vast majority of cases the results so far are showing that no horse DNA is present in the foods tested.
But this is still far from the full picture and we expect industry to continue to supply us with regular updates on their testing regime."
She explained why the watchdog tested for horse DNA down to a level of 1%, saying it was a level: "above which we think any contamination would be due to either gross incompetence or deliberate fraud; it’s not going to be accidental. Second, some laboratories can only test accurately down to a level of 1%.
‘But that does not mean that we’re not concerned with, or that we accept, levels below 1%. In terms of faith groups, there remains a significant issue about trace levels of other species below 1%. So we have a separate programme of work under way with Defra to look at the issues around that, too.
There are still more tests to come, but Brown, said it was industry's responsibility to get it right, not the government's.
"The results show that the overwhelming majority of beef products in this country do not contain horse. The examples we have had are totally unacceptable. But they are the exceptions.
"And as this programme of testing and publishing results continues, and as action is taken to tackle this issue in supply chains across Europe, we will reach the point where we can say with confidence that horse meat is no longer illegally entering the UK food chain."