My view is that if this ever ended up in court, one of the first things a judge is likely to look at is how it got there in the first place.
If West 28 and/or Trethowans can show they contacted you about the alleged debt, followed the Pre-Action Protocol and didn't get a response, then it's easy to see why they would have decided to issue a claim.
On the other hand, if you can show that you disputed the debt every step of the way, repeatedly asked for proof that you were liable and evidence that West 28th Street had the right to collect it, and those requests weren't properly answered, that puts you in a much stronger position. The same goes for any Subject Access Requests that weren't complied with, or any other failures to engage with the issues you raised.
At the end of the day, it's a bit like a game of chess. You're trying to put yourself in the best possible position by showing that you've acted reasonably throughout and made genuine attempts to resolve matters without court action.
That's really the whole point of the Pre-Action Protocol: to give both sides the opportunity to exchange information and try to avoid court if possible.
Ultimately, though, everyone has to decide for themselves how they want to deal with the situation.