The reality is that the only thing the EU can do is to is to walk away from any trade agreement or threaten some retaliation in some way. Agreements can only be enforced through economic/military power. I can’t see the EU invading the U.K. so an economic reaction is most likely. (Similarly the U.K. hasn’t invaded Hong Kong to regain it from China - although I’m sure there are a few there who long for the good old days).
The WTO adjudicates if a complaint is lodged by a country. This can take some years depending on the matters involved. It recently found against the US and its tariffs imposed on China.
It do not think it has any authority to penalise though as far as I'm aware. Only it gives aggrieved countries some justification to break their own rules against the offending country. And if the aggrieved country has allies, multilateral agreements can be created to impose harsher trade conditions on the offending country.
The problem is that with countries like the US, who is going to stand up against them when they break the rules?
The UK / EU is different. I get a sense that any type of trade war would be mutually self-destructive. More likely, future trade deals with third parties would be used as leverage to try resolve existing disputes.
Indeed from here: , the ECJ has consistently ruled to ignore WTO findings.
"To the disappointment of litigants and scholars alike,12 the European Court of Justice (ECJ), the highest court in the European Union on matters of EU law, has continually denied review of the legality of EU law on the basis of WTO law and has correspondingly denied damages to private enti- ties even when the EU’s behavior has been explicitly declared inconsistent with WTO obligations by the DSB".