When to stop responding to repetitive pre-action letters? At what point do I overrule my lawyers and decide to call the other side's bluff and stop responding?
There are no guidelines for neither the timing for, nor the pertinence of, ignoring pre-action letters. More important: You mention that your ex-girlfriend "has more money than sense", yet also you have been feeding lawyers for the easy job of addressing the repetitive letters instead of doing it yourself. You been harming yourself by delegating to licensed charlatans these ongoing tasks. Only you can put a stop to that.
Since the pre-action letters are repetitive, surely at this point you could study your lawyers' responses, get the hold of it, and respond to subsequent vexations accordingly. A decent lawyer would have told you this, similar to how lawyers routinely do copy/paste of legalese for plenty of unrelated, lookalike cases they handle.
Some comments to your post illustrate why you (and almost everyone) would be better off by doing it yourself (themselves) --provided you undergo a learning curve-- than through lawyers. Here, a user thinks your matter "is pretty easy - you can pay 200k now or 50k a year - if it’s going to take longer than 4 years, pay the 200k". Ironically, this came from the very same person who shortly thereafter told you he is an adjudicator, arbitrator, and mediator. Now combine that kind of frivolous & trivial approach with the aggravating factor that the lawyers you consult out there want your money.
Lawyers will keep telling you that you need them, but there is no rule that only lawyers may respond to lawyers. Thus, there is no legal impediment for you to respond to your ex-girlfriend's lawyer. You just need to know how to do it adequately, which is why your starting point to learn might be the responses that so far have cost you 50K. You could even represent yourself if the dispute goes to court. The concept of litigant in person is cognizable in England and Wales.
Litigation in person (aka pro se litigation, or litigation in pro per) entails a steep learning curve, a process that does not happen overnight. But good news is that laws (legislation, case law, and procedural law) are written in your own language, and are available online for free. It also helps that the ex-girlfriend has not filed suit yet, since that implies that you are not on a tight deadline to dispute her allegations and therefore you can focus on your learning.
There will be lawyers here who will dislike and downvote this answer, but you need to give a serious thought to the idea of --and preparations for-- litigation in person. Whether or not the ex-girlfriend's pattern turns out to be a bluff, you will be in a better position to discern with more accuracy the merits of a potential claim, the defenses thereto, the application of legal theories, how to advance your arguments in court, and so forth, without having spent another fortune on your personal lawyers' parade.