Owning your own home

Soundproofing - would a survey pick that up?

Nope. A surveyor will listen for 'noise and disturbance', but unless there's any happening while they're there they won't spot it. You need to do your own due diligence on this.

Here's what the survey for the place we're buying said:

No factors relating to noise or disturbances were noted during the course of the inspection. However, you may wish to carry out drive-past inspections of the property at various times during the day so that you can assess whether there are any factors which may affect the property.

So that's external noise but the question is how to assess internal noise at various times of day.