[broadgage]

I would be astonished if the supply was DC. DC mains "went out with the war" for new installations, and existing systems were largely extinct by 30 or 40 years ago.

If the house is to be let, then I see no alternative to a complete re-wire in full compliance with latest standards.
The regulations ARE in effect applied retrospectively for rental properties and are usually interpreted as requiring compliance with the latest rules including.
RCD/RCBO protection to all power socket circuits.
RCD/RCBO protection to lighting and other circuits if wired in shallow buried, non armoured cables.
Mains powered smoke detectors.

Replacing non earthed metal light switches with plastic might be acceptable for ones own use, but not for a rental.
Measured leakage of 10ma from a single switch is potentially dangerous and cause for serious concern. It represents the dissipation of well over 2 watts, easily enough to start a fire if concentrated at one point and long continued.

I would go so far as to recommend that the installation be isolated pending renewal.