So the All-4 & ITV-Hub branded streaming apps are available on the V6 box which runs TiVo software, but you're correct to point out these aren't on the TiVo box. While TiVo's are perfectly servicable, they are quite old now and never did support many apps due to their elderly hardware.
Some C4-boxsets are on VoD, but ITV only now support boxsets via their own app. So you've got 3 choices here..
1: Record these programmes when they're broadcast, and watch them that way
2: If you have VM broadband and would like the added facilities (and generally quicker box) that a V6 gives you, then call VM and ask about getting one. Your hand will be a lot stronger if you are out-of-contract and willing/able to renegotiate your entire package in exchange for a new 18month term.
3: Use the C4 & ITV streaming services online, as you already are.
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