Jake Humphrey has two jobs - presenting football on BT Sport and co-owner of production company Whisper Film. It's in the latter capacity that I expect him to do Channel 4 F1 coverage. It would also not surprise me if this was the prelude to a Channel 4/BT Sport split of coverage in 2018 (as distinct from the BBC/Sky split that previously reigned, or Channel 4/Sky that exists now).
Football coverage mostly got cut by the BBC last decade (one such cutback was what enabled them to get the F1 coverage when ITV bailed out in order to buy Champions League coverage). The two parts the BBC still has are partial coverage of the two big international tournaments (the Euros and World Cup) and "Match of the Day" - a highlights show covering the best bits of all English League football (and, in Scotland, Scottish League football too). The latter will survive any number of cutbacks - even if the entire Sport department was canned, they'd find a way to fund it through "Entertainment" or something, because it's that much of a lynchpin for part of its audience.