This is true if you want to operate in in Class A, B, C or E airspace; or above 10 000 feet above mean sea level in Class G airspace.
See here for a the brief version and the linked Reg for the full version:
Mode S transponders, ADS-B and VFR aircraft | Airservices
However note that under this CAO this only applies to aircraft "
modified by having its transponder installation replaced on or after 6 February 2014", thus you can fit any new parts you want to an existing installation:
Also Para 9E.3 exempts an aircraft which does not have "sufficient engine-driven electrical power generation capacity to power a Mode S transponder" which may apply to a cub depending on configuration.