Of those two, the Carrera is the better bike. The Coyote looks nasty and probably weighs a tonne (hi-tensile steel frame and pretty basic components). Halfords may not have the greatest reputation for bike service, but I'd also be wary of Evans these days, as they've been taken over by Mike Ashley.
However - no idea whether this is the case in London as I'm nowhere near, but round my way, Carreras seem to be thieves' number one favourite bikes to steal, and a shiny new one without a couple of very good locks wouldn't last long. For something for daily city use, I'd definitely lean towards used rather than new.
On the secondhand option: do you have a secondhand bike place/charity near you? I've no experience of London, but most cities have some sort of place that refurbishes donated bikes and sells them on. £200 would go much further second hand than it would new, and a bike from one of those places would have the benefit of having been serviced before sale.
FWIW, a few years ago I also commuted a ~6 mile round trip; I did it on an old Raleigh Pioneer I bought second hand for £20 and gradually replaced/upgraded bits as they wore out. Decent old early '90s Reynolds 501 steel frame, old but serviceable Shimano groupset, bombproof but unappealing to thieves. I eventually gave it away to my local bike charity because I no longer commute and needed the space, but it worked just fine.