I contacted the official department for Border Control because the question of wigs & airports came up a lot.

Their response was that if the wearer set off the metal detecting alarm & the source was found to be their head (through attaching their piece with metal clips) they would be asked to under go a 'pat-down' on their head.
This could be done publicly or privately, depending upon the wishes of the wearer.

They were reluctant to specifically say whether a wig could or couldn't be detected with the body scanners but they confirmed that in normal circumstances, the detection of a wig wasn't a cause for suspicion or investigation and that they are duty bound to protect the dignity & privacy of travellers.