Hundreds of British sheep farms – all but eight of them in Wales – could next year finally see the end of safety measures imposed as a result of radioactive fallout from the nuclear disaster at Chernobyl 25 years ago.

The Food Standards Agency (FSA) is proposing lifting restrictions originally placed on 9,800 upland farms and more than 4m sheep in north Wales, including in the Snowdonia national park, Cumbria, southern Scotland and Northern Ireland after rain clouds dumped contaminated material from the blast in Ukraine, then part of the USSR, 1,600 miles away.

The agency says the risk from radioactivity to consumers eating lamb or mutton is now "very low" and that controls on 334 farms in Wales, some no longer with sheep on them, and eight in Cumbria should be lifted. The FSA launched a formal consultation on its proposal on Thursday. This closes in February so restrictions still involving about 250,000 sheep will not be lifted until well into next year.

Since June 1986 when the present restrictions were imposed, farmers have had to call in officials to check their sheep for caesium, the main radioactive element, every time they want to move the animals off the hills for market. The Chernobyl blast happened on 26 April and the fallout first arrived in Britain during the first weekend in May. Radioactive caesium remained in the uplands soil and grass and sheep that graze there can often only decontaminate themselves naturally after being moved to lower non-radioactive pastures.

Sheep on affected farms have had to be tested to ensure they do not have radiocaesium levels above 1,000 becquerels a kg. Those that pass are allowed to be slaughtered for food. Those that fail are marked with dye and can leave restricted areas but cannot be slaughter for at least three months. But checks over the summers of 2010 and 2011 suggest that radiocaesium levels are now rarely exceeded at a time they might be expected to be at their highest.

Farmers get £1.30 a sheep each time they present stock for testing. Cattle and other livestock have not been of concern because they graze at lower levels, although for a short time after the fallout arrived in Britain, low levels of caesium were found in mushrooms and honey.

The cost to authorities of carrying out the checks fell sharply as thousands of farms were cleared to operate normally, but even last year the bill is thought to have been about £620,000.

The Welsh government welcomed the move, saying: "While food safety is of paramount importance both in terms of public health and for continued confidence in the Welsh farming and food sector, we support the evidence-based approach the FSA have taken to assessing risk of exposure to the public from the effect of the Chernobyl nuclear disaster."

Its statement added: "Levels of radiocaesium recorded in sheep have fallen well below the level of any serious risk to the consumer, and the controls currently in place go beyond the already stringent European food safety law requirements - which could be viewed as overly restrictive."