In Statutes of limitations and the pre-action protocol (PAP) it is stated that the "pre-action protocol (PAP) must be completed before a case is brought to court in England-and-Wales. Just what is the "pre-action protocol" in E&W, when is it required, and how long does it typically take?
The pre-action protocols are part of the Civil Procedure Rules (CPR) which governs proceedings in the County Court, High Court, and Court of Appeal (see Rule 2.1).
They set out what the parties should do before initiating proceedings in court. Being practice directions, they are not rules, but you ignore them at your peril; failing to do so will not affect the outcome of your case but can have cost implications or, in the most severe cases, result in sanctions (see paragraphs 13 - 15 here).
There is a general pre-action protocol and a set of specific pre-action protocols for particular types of cases. If there is a specific protocol for your case, you follow that, otherwise you follow the general one (see paragraph 2).
The full list of specific pre-action protocols can be found here. Note that there is another list contained within the general pre-action protocol at paragraph 18 but this list is not complete. This is rather unfortunate because paragraph 18 contains the phrase "the table sets out the protocols currently in force" and, below the table, "Updated: Wednesday, 6 April 2022" (which implies, incorrectly, that any older protocols not appearing in the table are not currently in force). I suggest using the first list.
"How long does it typically take?"
This varies depending on the protocol being followed. See for example paragraph 6 of the general protocol which, without being prescriptive, suggests that a reasonable time for a defendant to respond to a pre-action letter is 14 days in a simple case and 3 months in a complex one.
"pre-action protocol (PAP) must be completed before a case is brought to court in England-and-Wales"
This is incorrect. Per paragraph 17 of the general pre-action protocol, if you are close to the limitation period, you can start proceedings and then apply for a stay to give you time to comply with the protocol.