Ministers are struggling to reassure consumers over the horsemeat scandal after tests revealed potentially dangerous contamination of meat with veterinary drugs and Asda confirmed the first trace of horse had been found in a fresh beef product.

Overwhelmed laboratories are warning that the industry may not fully comply with Friday's deadline for completing tests for horse in all beef products, raising the prospect that the government will be unable to give British food a clean bill of health for days.

Medical risks from eating horse containing the equine painkiller phenylbutazone, or bute, are said to be very low but David Heath, the food minister, revealed on Thursday that eight horses slaughtered for food in the UK had tested positive. Six of those carcasses had been exported to France for use in human food in the last few weeks, according to the Food Standards Agency, but efforts were being made to recall them.

The Guardian has also learned that two positive tests for bute in 2012 were not reported to the Food Standards Authority (FSA) for seven months.

On Thursday police arrested three men on suspicion of offences under the Fraud Act as part of their investigation into the mis-selling of horsemeat as beef. Dyfed Powys police said they were being held at Aberystwyth police station following arrests at abattoirs in Wales and Yorkshire.

One of the men was named as Dafydd Raw-Rees, 64, the owner of Farmbox Meats Ltd near Aberystwyth, who was held with a 42-year-old man. A third man, aged 63, was arrested at the Peter Boddy Licensed Slaughterhouse in West Yorkshire. The FSA suspended operations at both sites after raids at the premises on Tuesday on suspicion that the plants sold horsemeat for use in burgers and kebabs.

In a further sign of the severe damage the horsemeat scandal has caused to consumer confidence, 11 of the UK's biggest food suppliers, including Tesco, Asda, Sainsbury's, the Co-operative, the Compass group and Brakes, issued a public letter on Fridayin which they stated they shared food shoppers' "anger and outrage", although the letter stopped short of an apology.

"We are working around the clock to complete the most comprehensive testing of processed beef products ever undertaken, anywhere in the world," it said. "We will do whatever it takes to restore public confidence in the food they buy and eat."

Asda has withdrawn its fresh beef bolognese sauce after tests for horse DNA came back positive. It is the first time since the horsemeat scandal unfolded that horse DNA has been found in fresh produce.

The supplier, Greencore, based in Bristol, also provides beef to Sainsbury's and pork to the Co-operative but both companies are keeping products containing the meat on the shelves.

Asda has removed the Chosen By You 350g Beef Bolognese Sauce from stores across the country along with beef broth soup, meat feast pasta sauces and chili con carne soup, also from Greencore, as a precaution.

Asda said: "As you'd expect, we are withdrawing the beef bolognese sauce from our shelves with immediate effect. In line with the belt-and-braces approach we've taken from the start, we're also withdrawing three other products from the same supplier as a precaution."

Sainsbury's said it would keep two own-brand bolognese sauces supplied by Greencore on its shelves because the meat used by Asda is from Ireland, while its meat is from Britain. It added: "We have already carried out tests on a range of our beef products including burgers, ready meals and minced meat and no trace of horse DNA has been found in any of our products."

The Co-op said products supplied by Greencore were still being sold.

Greencore confirmed traces of equine DNA had been found in the meat in the sauce which had been supplied by an ABP Food plant in Tipperary Ireland. It said was working with the company to carry out further tests to determine the extent of the equine DNA.

The environment secretary, Owen Paterson, has ordered all food companies to test their processed beef products and deliver the results by Friday, but the number of tests required rapidly overwhelmed the capacity of testing laboratories. Paterson subsequently expressed the hope of enough "meaningful" results to get a picture of the size of the problem in Britain.

One food industry source suggested "a good number of hundreds" of results would be available from major retailers and manufacturers but the FSA said only that "more than a hundred" results had come in. Products being tested include burgers, meat balls, lasagnes, bologneses, cottage pies, sausages and others containing mince.

A spokesman for the British Retail Consortium, representing major supermarkets, said: "There is no question this has been putting enormous demands on the testing facilities available."

Laboratories have been working round the clock, but with large supermarkets likely to have 300 to 500 affected product lines and multiple samples needed to confirm freedom from adulteration, the scale of the testing has proved overwhelming, according to experts.

"It is unacceptable that bute at any level has been found in horsemeat," Heath said, adding that the cause of the contamination was being investigated.

The shadow environment secretary, Mary Creagh, asked of bute contamination in parliament on 24 January: "Can the minister explain why, up until four days ago, all horses were being tested for bute but were still being released for human consumption? In the middle of a horsemeat adulteration scandal, that is catastrophic complacency."

Dame Sally Davies, the UK's chief medical officer, said there was very little health risk. "The trace levels detected are very unlikely to have harmed any human, child or foetus." She suggested a person would have to eat more than 500 horsemeat burgers to get a harmful dose.

No bute is allowed in horsemeat for human consumption as there is no accepted safe level. In July 2012 the Veterinary Residues Committee (VRC), which advises the government, warned that it had "repeatedly expressed concern" about bute entering the food chain because it had the "potential for serious adverse effects in consumers".

The FSA also tested Findus lasagne, Tesco burgers and other food products found to contain horsemeat for bute contamination, but found no positive results.

The horse passport system meant to prevent bute contamination in the 9,000 horses slaughtered for meat in the UK each year was not working, a member of the VRC told the Guardian.

FSA chief executive Catherine Brown said this was because people were "breaking the rules" and accepted the test results indicated that "there has been a significant amount of carcasses with bute in going into the food chain for some time".

The FSA tested all 206 horses slaughtered in the UK for food between 30 January and 7 February for bute, at a cost of £415,000, and found eight positive results. In two cases the meat did not leave the slaughterhouse but six horses were sent to France.

That rate of contamination would mean hundreds of affected UK horses entering the food chain every year. Only 145 tests were conducted in the whole of 2012 and about 50 a year before that.

The FSA said that, from now on, horse carcasses would not be released from abattoirs until they had received a negative test. Brown said this was now possible because the time taken to get test results had decreased from 14 days to 48 hours.

However, the FSA did not test for any other possible contaminants. Michael Walker, a founder board member of the FSA and now at the privatised laboratory LGC, warned other chemicals could be present, given that the scandal was very likely the result of fraud:. "Fraud is outside the normal safeguards," he said. "A fraudster isn't going to worry about other issues such as chemical or microbiological safety."

In the case of the two carcasses that tested positive for bute in 2012 and were not reported to the FSA for months, the horsemeat is thought to have left abattoirs in May and October but the positive results did not arrive at the FSA until 10 days ago. In the meantime the meat had gone to the Netherlands and France. The government agency that commissioned the tests, the Veterinary Medicines Directorate, said it had submitted the results to the FSA, as soon as they were confirmed. The FSA said it "did not receive these two results".