The TiVo has access to the same OnDemand library as any other VM box, which includes all ITV "CatchUp" & Boxset programmes.
Unfortunately, there's no getting around the TiVo being an old box that can struggle with the various streaming apps. That's one reason why many of these new apps (Prime, ITV-Hub, All-4, My5) are available on the V6 box which is much more capable of running them.
Depending how long you've had your current package, and assuming you have Virgin broadband (which is a requirement) you may be able to swap to a V6 as part of a new bundle deal.
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