The UK Parliament's Joint Committee On Human Rights has changed its mind (an earlier report adopted a wait-and-see litigation-focused approach) and now urges a legislative clarification of the meaning of public authority. Specifically, it urges a separate interpretive provision (not amending the HRA itself) to the effect:
"For the purposes of s. 6(3)(b) of the Human Rights Act 1998, a function of a public nature includes a function performed pursuant to a contract or other arrangement with a public authority which is under a duty to perform the function."
Of course, the pending appeals to the House of Lords may render this moot. But the JCHR seems not to be holding its breath.