The courts have moved away from the idea that the imposition of ADR upon parties would be a breach of the right to fair trial (Halsey v Milton Keynes NHS Trust (2004) EWCA Civ 576) or that ADR can only be undertaken with the parties consent (Parker J, Lomax V Lomax  EWHC 1267 (fam)).
Recent case law shows that to ignore an invitation to mediate can be a trap to the unsuspecting Defendant and an expensive omission:
PGF II SA v OMFS Company 1 Ltd  EWCA Civ 1288,  1 WLR 1386,  (Briggs LJ):
Here the Claimant was compelled to accept the Defendant's early Part 36 offer out of time. In the normal course of things the Claimant would pay the Defendant's costs post the date of expiry. Not so here. The Claimant had made a request that the parties mediate to attempt resolution, an offer that was ignored by the Defendant. It is the duty of the recipient to respond constructively. To ignore such a suggestion is tantamount to unreasonable conduct and the disapplication of Part 36 principles. The Claimant walked away without having to pay the Defendant's costs.
Gore V Naheed  EWCA Civ 369: This case involved a property dispute where the Claimant tried for 6 months to get the Defendant to agree to mediate to no avail. The Claimant recovered less than the Defendant however the Claimant was awarded 75% of their costs because the Claimant's efforts to engage in ADR were ignored. Where the parties were not that far apart it was nonsensical to fail to mediate.
There has been somewhat of a revolution over the last 11 months and a movement towards the Courts ordering that the parties mediate:
The effect of CPR r.3.1 (2) (m) as to whether consent was required was swiftly overturned by the Court of Appeal in Lomax V Lomax  EWCA Civ 1467. It determined that the wording in r.3.1 (2) (m) did not contain a requirement for the parties to consent to Early Neutral Evaluation (ENE). ENE was not an obstruction to parties' access to the courts; it was part of the court process.
BXB v Watch Tower And Bible Tract Society Of Pennsylvannia (2020) EWHC 656 (QB): The Defendants had breached a court direction given in standard form, to serve a statement explaining their refusal to participate in a joint settlement meeting. That was unreasonable conduct and the costs incurred by the claimant from the date of that refusal were assessed on an indemnity basis.
DSN V Blackpool FC (2020) EWHC 670 (QB) Griffiths J: A defendant which had refused to engage in mediation because it was confident in the strength of its defence was required to pay some of the costs on the indemnity basis when the claimant beat its Part 36 offer. No defence, however strong, justified on its own a failure to engage in alternative dispute resolution.
As can be seen by Sir Geoffrey Voss' introduction to the March 2020 Edition of the White Book, there now seems to be an appetite for a re-evaluation of the Courts' powers in respect of ADR. In the meantime, the parties should take heed and ensure that an invitation to attempt resolution through mediation or similar process is not ignored but acknowledged and responded to constructively.