I suppose this question could be put more succinctly as Does the United Kingdom have a known traveller programme, like ANZ SmartGate or the North American NEXUS/Global Entry? Indeed, they do: the Registered Traveller service.
Frequent visitors and some visa holders who are adult nationals of Australia, Canada, Japan, New Zealand, and the US can apply. According to the promotional video, users
- don't have to fill in landing cards
- may use faster European Economic Area (EEA) border queues
- may use ePassport gates at participating UK international ports if they have a biometric passport
Per the website, the express queues are avaialble at Edinburgh, Gatwick, Glasgow, Heathrow, London City, Manchester and Stansted airports, and Brussels, Lille and Paris Eurostar terminals. The annual subscription is £70, though if your application is denied, £50 of that will be refunded.