Simple answer: Take a breath, forget it, do something nice instead.
BT or any phone company doesn't really act on individual cases like this, but they will add "anonymous call reject*" for £5.40 a month, although free to vulnerable groups by special arrangement but watch bills closely as the charges have re-appeared sometimes. Other providers charge a couple of pounds a month, TalkTalk's phone privacy features have been free since their hacking issues a while back.
Partial or unavailable numbers will still get through and even if rejecting withheld numbers and registering on the telephone preference service, overseas call centre are not bound by it as there is no enforcement mechanism, and it's also quite a lot of effort complaining to Ofcom who can only act against entities in the UK anyway (possibly Europe by referral). You are required to present a lot of evidence to show harassment/nuisance/distress rather than persistence from callers.
Companies who's primary line of business is surveys can also ignore the TPS, although "Did you have PPI?" is not a survey.
Just one thing to bear in mind, the caller is usually on minimum wage, with a horrible boss and a target to meet, so politely disengaging straight away rather than giving information or abuse is probably best. Sounds like your wife knows the drill.
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TG
* Anonymous call reject might block genuine incoming calls such the appointments service at the local doctors if they withhold their number.