I thought this might be of interest in case someone else has extra information or has a connection to this family ..
The 1710 Fleet marriage for Charles Constable & Phillis Rain states that he was a periwigmaker.
In Norfolk in 1713 a Charles Constable takes an apprentice (Joseph Freezer?) as a Barber & Periwigmaker
In Norfolk 1712 - 1730 Charles & Phillis Constable's children, all Bp at St Michael Coslany.
Norfolk: Charles Constable (married man) buried 1736 St Michael Coslany
Norfolk: Phillis Constable - widow - buried 1756 St Michael Coslany
Obviously there could be 2 men named Charles Constable who were Periwigmakers but the coincidence was worth checking.