If we take it as "Heavy Rail where all services start at Station A, all services terminate at Station B, all services run on the same double track railway (but stopping pattern at intermediate stations can vary)" as a definition then Liverpool Street to Shenfield is the clear winner...
...the Cardiff Bay shuttle takes "silver"...
the "bronze" is tied between Edinburgh - Glagow Queen Street or one of the single Merseyrail services (which are generally all fifteen minute frequencies apart from Ellesmere Port) - unless you want to argue about whether Merseyrail is 100% on Network Rail track, if that is one of the criterion to differentiate Heavy Rail? (due to the long term maintenance of the infrastructure being in PTE hands IIRC?)
(excluding Heathrow Express?)