NDA's and Non-Competes are notoriously difficult to take legal action against. As you mentioned the sheer cost of the lawsuit and appeal process could far outweigh the benefits of actually winning. But ultimately it is indeed a binding contract, and a valid one that can be very effective when you have the money there to enforce it. Typically, the judge does favor judgment to the complaining party.
One thing that I know can be done, at least in the US, is to file a motion with a court to ask it to issue an injunction against the offending party. Sometimes this can be done without a lawyer with a Magistrates court, but then be prepared for a back and forth, of we need more proof why I should issue this. If the software was blatantly stolen, it should be easy enough to show both applications side-by-side.
This then freezes their software application in it's tracks until the matter is resolved, either through an agreement or through the courts. Which, you might still never get damages because of the overall cost, but at least neither will the offending party.
Laws are different everywhere and you being from GB, so I can't speak to the validity of this method across the pond.
Note: I am not an attorney, and please seek one to validate any advice herein.
Hope this helps.