Thank you for all the replies.
I have tried in the headset in multiple A380s the older aircraft seem to have less of an issue, but this is not consistent. I have another adaptor from long ago, which I can have a crack with.
The headset doesn't have ANR, but it does have a box which a phone can be plugged into or listen to music. This requires a small watch battery to power.
Additionally the cabling of the headset looks simple, so I doubt it has any shielding its self. Is it possible to add some sort of wrap?
I do notice a quiet background noise when I connect the headset through the cockpit speakers, which stops when I pull the headset out.
I have also used other types of headset and no sound issues with those.
I'm not flying for a week, but I will give the other suggestions ago and let you know.
Thanks again.