The UK could still have standards, but (from a CATO paper on regulatory protectionism)
The General Agreement on Tariffs and Trade (GATT), one of the WTO’s
core treaties drafted in 1947, does not stop at border measures but
also requires national treatment of imports; that is, governments’
domestic laws must treat imports the same as goods produced at home.
This kind of thing can get tricky, since clever regulatory capture subtly takes ideas that seem to be defending consumers and promote them to the extent that their main effect is squashing competition. For example:
The U.S. Food, Conservation and Energy Act of 2008 (popularly known as
the “2008 farm bill”) included provisions requiring country-of-origin
labeling (COOL) on all imported beef, chicken, lamb, pork, and goat
meat and certain perishable commodities sold in retail outlets in the
United States...
A WTO panel found, and the Appellate Body confirmed, that mandatory
COOL rules violate Article 2.1 of the TBT Agreement by treating
imported livestock and meat from Canada and Mexico (the two
complainants in the case) less favorably than similar domestically
produced products. According to the Appellate Body report, the burden
of maintaining detailed records, which caused harm to foreign
livestock producers by increasing their costs, was not justified by
the goal of informing consumers, because the information ultimately
given to consumers was much less specific than what the processors
were required to keep track of. This disparity sufficiently revealed
the protectionist nature of the law.
Another example comes from anti-smoking regulation
In 2009 the Family Smoking Prevention and Control Act banned the sale
of all flavored cigarettes in the United States, except menthols. Why
the exception for menthols? It’s not because menthol cigarettes have
fewer negative effects than other flavored cigarettes or because
menthol cigarettes are less favored by new, underaged smokers than
clove cigarettes. No, there are two reasons menthols were excluded.
One, because they are popular—25 percent of all cigarettes smoked in
the United States are menthols—especially among African-Americans (80
percent of black smokers choose menthols). And two, because a ban on
flavored nonmenthol cigarettes did not affect U.S. cigarette
producers, only their foreign competition. The result was a ban on
less popular flavored cigarettes from Indonesia but not on the
flavored cigarettes made in the United States.
The WTO found this law also to be inconsistent with U.S. obligations
under the TBT Agreement. Here, the Appellate Body considered that
prevention of youth smoking was a legitimate goal. They even accepted
that treating cloves less favorably than menthols would be acceptable
if that different treatment was based on a “legitimate regulatory
distinction.” But they also recognized that exempting menthols did
not further the stated goal of the regulation, because there was no
evidence that young people would not choose to smoke menthols instead
of cloves.
These examples come from the United States and the notably pro-trade CATO institute, but they illuminate how the WTO looks at product standards and regulations.
So under WTO rules, the UK can still have product standards. These product standards cannot, however, be tariffs in disguise. They cannot impose a regulatory burden on foreign importers and not domestic ones without a compelling reason.