Third party rights: effect of arbitration on third parties

The Contracts (Rights of Third Parties) Act 1999 abolished the doctrine of privity of contract and (subject to contrary agreement) allows a benefit to be conferred upon a non-contracting party. How is that benefit to be given effect if the contract itself contains an arbitration clause?

A partial answer is given by section 8 of the 1999 Act, which applies where the claim is brought by the third party and requires him to comply with any arbitration clause. But what if the claim is brought against the third party and there is nothing in the contract which entitles him to rely upon the arbitration clause? Blair J in Fortress Value Recovery Fund I LLC v Blue Skye Special Opportunities Fund LP [2012] EWHC 1486 (Comm) held that the arbitration clause is inapplicable in such circumstances.