ITV Hub comes in a few different versions depending on what you're watching it on. Presume its not Sky you're watching it on since that doesn't have adverts. Is this on the website? A smart TV app? Something else?
There are known buffering problems with loading adverts in at the end of parts, particularly on the Vestel platforms (JVC, Hitachi etc). I don't think it's a case of the processor not being up to it, but if connection sppeds are borderline it seems to happen more often, speaking as someone who gets the same problems regularly on UKTVPlay.
The Now TV version of the app has a bug where the Part 1 scene ends but instead of the ad break playing, you get a few seconds of Part 2 before the ads abruptly kick in.
Similarly, at the end of the ad break, the app plays the last few seconds of Part 1 again before starting Part 2.
Have you tried contacting the ITV Hub tech support if there's one? Britbox, for example, is very good and normally replies to tech problems and queries within a few hours when I've need assistance.