Meat Promotion Wales – Hybu Cig Cymru (HCC) warned research suggested British branding on products like lamb and beef could be a disadvantage in key markets.
Farming unions have supported the call.
The Welsh Conservatives said both flags should be used to promote Welsh produce abroad.
After Brexit, the UK Government intends to develop its own trade policy, and food and farming organisations have been lobbying hard about how their produce should be marketed.
The value of Welsh food and drink exports exceeded half a billion pounds for the first time in 2017 – with 77.3% destined for the EU.
A third of Wales’ lamb and 97% of its shellfish was sent to the continent, or further afield to countries like South Korea, through EU trade agreements.
Gwyn Howells, HCC’s chief executive, said the British brand currently had “little traction” in key markets for Welsh farmers and putting it on Welsh red meat exports in particular would “absolutely” be a disadvantage.
He pointed to a recent survey of 4,503 international consumers by the Agricultural and Horticultural Development Board (AHDB), which suggested a more negative perception of British food than positive in France, Germany, Japan, the USA and Canada.
BBC Wales understands no equivalent research has been done on international perceptions of Welsh food, but Mr Howells claimed “the Welsh offering” had more recognition and was “vastly more welcome” in these markets.
“We must prioritise the Welsh dragon – it’s much more than a logo. It’s a promise of where it has come from, the landscape of Wales, the traditional methods used to produce food to the highest standards, which adds value.”
However, in India, China, Saudia Arabia and UAE, where AHDB survey feedback on British food was more positive than negative, he said there was arguably a role for deploying the union flag to try and gain access for Welsh producers – what he called “a twin-track approach”.
NFU Cymru director John Mercer said Wales had “a fantastic story to tell” in terms of branding and that ministers should think carefully about what would appeal to different markets.
FUW President Glyn Roberts said the AHDB report also showed that quality and price are the highest priority for consumers, and that the Welsh brand should be promoted to reflect “the top quality food we produce at environmental and animal welfare standards that are second to none – and do so in a way that avoids additional burdens and costs for farmers and others”.
Post-Brexit plans are also under way for a British system to protect certain food names like Welsh lamb, Anglesey sea salt and Carmarthen ham – to replace designations currently awarded by the EU.
Ministers in Westminster sparked controversy in July after their sponsorship of the food hall at the annual Royal Welsh Show in Powys – Europe’s largest agricultural event – saw the slogan “Food is Great” and union flags displayed on advertising.
Environment Minister Lesley Griffiths insisted she did “not want to see the union jack on… our big shop to the world”.
But Andrew RT Davies AM, Welsh Conservatives spokesperson on the environment and rural affairs, said Wales should be “embracing both brands”, and described Ms Griffiths’ remarks on the Royal Welsh Show controversy as “bizarre”.
“We need to be led by the marketeers – we have the great opportunity to use two marketing platforms, let’s not rule one out,” said Mr Davies.
A Welsh Government spokesman said Wales’ food and drink industry had enjoyed success, gaining recognition for its food producers.
“We believe post-Brexit it will be a priority to authentically brand food and drink production in Wales as truly sustainable, which can be independently verified.”
The UK Government said the status of protected produce, including from Wales, would automatically become part of the UK geographic indications (UK GI) scheme following Brexit to ensure “their unique heritage and quality is safeguarded”.
“In addition to the new UK GI logo, producers can add additional labels, such as the Red Dragon, at their discretion,” added an official at the Department for Environment, Food & Rural Affairs.