It sounds exactly like "How do you do it?" to my ears. There's nothing amiss about the accent; the interviewer has a regular clear British accent. Some of your questions need correction (please take the time to get this right; it's elementary English): "Why does he keep pronouncing 'do' as 'to' in this video?" "Why does he pronounce it like this?" "Which regional accent is it that pronounces 'do' like this?"

I hear exactly what you're talking about! As an American, the "t" sound seems very prominent to me. I think it's because "do" is a very small word in between two vowel-heavy words. It's probably just very easy to use the "t," which is the voiceless pair for "d" (which is voiced). That's my guess anyway. But yes, I agree it sounds like "t" here and definitely not "d."

He says 'You're an actress, and you also study at Cambridge. How do you do it?' His pronunciation is absolutely normal and clear, and he has no noticeable regional accent, Like Lily Cole, the interviewer has neutral, Southern English/RP pronunciation. There is nothing unusual about his pronunciation at all. Listen again, and you'll hear that what I've written above is what he says.