There is nothing to prevent your friend recording face to face conversations in his own house and he has no requirement to warn a person to whom he is talking that it is being recorded. None of the social worker's "rights" have been breached. If he wanted to keep what was said private he should have said so before the conversation started. People are entitled to discuss their affairs (including details of conversations they have had with officials) with anyone they choose. The conversation, in that respect, is not "private". The rules applying to formal interviews such as those conducted under "PACE" do not apply.
Whether such a recording could be used in court proceedings is less clear. There is no blanket ban and the circumstances would be heard by the court before a decision to allow the recording was taken.
I could see no objection if it was being used simply to settle a dispute over what was or was not said. It is no different to you telling the court what was said and it is a lot more reliable. I find it very odd (though not at all surprising) that someone from Social Services would hold a conversation with somebody but then, in the event of a dispute, resist efforts to have evidence produced to prove what was said. As Chris suggests above there is nothing “unfair” about such a recording (provided your friend has not coerced or led the social worker to say things he may not have said unless so led). What would be unfair is if something prejudicial to your friend’s case was said and it could not be proved and a court may well decide that aspect is more important than protecting the Social Worker.