As you might well be discovering, Horizon V360 is a totally different TV platform to TiVO.
Horizon is the system used by VMs parent company, a Europe wide cable operator. In the rest of Europe broadcast radio ceased to be carried on cable systems at digital switchover in 2000, hence there is no ability to record it on the platform. Virgin has an interim measure where some broadcast radio is available from the main menu on V360, but these stations are diminishing as radio groups such as Bauer move away from broadcast format in the UK as well.
The best way to get radio on V360 is via the Radioline & BBC Sounds apps, where you will also find some catch-up content.