In light of recent court cases many might agree that the answer to this question is "no". That said, Sir Alan Ward in the case of Wright v Michael Wright Supplies Ltd1 commented that:
"You may be able to drag the horse (a mule offers a better metaphor) to water, but you cannot force the wretched animal to drink if it stubbornly resists. I suppose you can make it run around the litigation course so vigorously that in a muck sweat it will find the mediation trough more friendly and desirable. But none of that provides the real answer. Perhaps, therefore, it is time to review the rule in Halsey v Milton Keynes General NHS Trust ... Perhaps some bold judge will accede to an invitation to rule on these questions so that the court can have another look at Halsey in the light of the past 10 years of developments in this field."
So as a starting point, it is important to remember that the courts cannot2 compel a party to mediate. One of the reasons that the court does not have jurisdiction to order parties to mediate against their will is it would be a violation of Article 6 of the European Convention on Human Rights. However, there is no doubt that the current judicial climate is such that, whilst parties cannot be forced to settle their disputes by means of ADR, they are strongly encouraged to attempt to do so. This all flows from the case of Halsey v Milton Keynes General NHS Trust3 where Dyson LJ said:
"Parties sometimes need to be encouraged by the court to embark on an ADR. The need for such encouragement should diminish in time if the virtue of ADR in suitable cases is demonstrated even more convincingly than it has been thus far. The value and importance of ADR have been established within a remarkably short time. All members of the legal profession who conduct litigation should now routinely consider with their clients whether their disputes are suitable for ADR. But we reiterate that the court's role is to encourage, not to compel. The form of encouragement may be robust..."
This pro-ADR climate is firmly reflected in the CPR, the Pre-action protocols, the TeCSA ADR Protocol, Lord Jackson's ADR Guide and the 3rd Edition of the TCC Guide, which came into effect on 3 March 2014. Section 7 of the TCC Guide reinforces the importance of Halsey and places an obligation on legal representatives to ensure that their clients are fully aware of the benefits of ADR. It also makes express reference to arguments on costs associated with a party's unreasonable refusal to mediate. Parties and those advising them have been warned. Section 7 of the TCC Guide notes that:
"7.1.1 The court will provide encouragement to the parties to use alternative dispute resolution and will, whenever appropriate, facilitate the use of such a procedure... In most cases, ADR takes the form of inter-party negotiations or a mediation conducted by a neutral mediator... The parties are advised to refer to the ADR Handbook. 7.1.3 Legal representatives in all TCC cases should ensure that their clients are fully aware of the benefits of ADR and that the use of ADR has been carefully considered prior to the first CMC. 7.2.1 ADR may be appropriate before the proceedings have begun or at any subsequent stage. However the later ADR takes place, the more the costs which will have been incurred, often unnecessarily. The timing of ADR needs careful consideration. 7.4.1 Generally. At the end of the trial, there may be costs arguments on the basis that one or more parties unreasonably refused to take part in ADR. The court will determine such issues having regard to all the circumstances of the particular case. In Halsey v Milton Keynes General NHS Trust  EWCA Civ 576;  1 WLR, the Court of Appeal identified six factors that may be relevant to any such consideration:
(a) the nature of the dispute; (b) the merits of the case; (c) the extent to which settlement methods have been attempted; (d) whether costs of the ADR would be disproportionately high; (e) whether any delay in setting up and attending the ADR would have been prejudicial; and (f) whether the ADR had a reasonable prospect of success.
Further parties should consider the merits of ADR at an early stage. Paragraph 5.4 of the Construction Pre Action Protocol makes it clear that parties should review whether "some form of alternative dispute resolution would be more suitable than litigation at the pre-action meeting."
In Burchell v Bullard,  EWCA Civ 576 Ward LJ said:
"The parties cannot ignore a proper request to mediate simply because it was made before the claim was issued. With court fees escalating it may be folly to do so. I draw attention, moreover, to para 5.4 of the pre-action protocol for construction and engineering disputes, which I doubt was at the forefront of the parties' minds, it should preferably apprise the parties to consider at a pre action meeting whether some form of alternative dispute resolution procedure would be more suitable than litigation. These defendants have escaped the imposition of a costs action in this case but defendants in a like position in the future can expect little sympathy if they blithely battle on regardless of the alternatives".
However, parties should not assume that the courts will always accede to a request for a stay to the court timetable to enable there to be a mediation. In the case of CIP Properties (AIPT) Ltd v Galliford Try Infrastructure Ltd4, it was suggested in this case, that a three or four month stay for ADR be built into the court timetable. As Mr Justice Coulson said, often at a CMC, one or more of the parties will seek a stay of the proceedings whilst they endeavour to resolve their disputes by way of mediation or some other form of ADR. There can either be an application for an immediate stay, or for a stay further down the line, sometimes after disclosure or after the exchange of witness statements or expert's reports. Mr Justice Coulson further noted that:
"The judges in the TCC set great store by ADR. Disputes like this one are time-consuming and therefore expensive to fight out in the traditional way. Even if the court adopts all the various techniques for reducing the trial to a minimum (such as 'hot-tubbing' the experts and carefully timetabling the cross-examination), trials are often unwieldy and cost-inefficient. Expert's fees often account for a large proportion of the costs. A professional mediator, engaged at the right time in the...