Hmm. I've used both Specsavers and Vision Express. Neither of them could provide me with glasses inside a week, but then I do have a very non-standard prescription (mainly varifocals). If you have a high prescription, lots of astigmatism and need varifocals (because you have had cataract operations) then you have no hope of getting a rapid service.
I went to Dollonds when I moved to Tamworth (there wasn't a Vision Express there at the time) and they were OK but not brilliant. They were particularly not OK when you wanted sports specs e.g. prescription ski goggles, swim goggles and sunglasses for cycling and other activities. In the end I went to Philip Howards in Tamworth, a local small franchise. They were absolutely excellent. My specs took 1-2 days but more to the point they have managed to do prescription ski goggles that don't look prescription, fantastic Adidas sports sunglasses and prescription swim goggles all without blinking an eyelid (pardon the pun). It is worth the wait to get what you really want. For ordinary specs with standard lenses, no varifocal, and not a very high prescription I'd choose Vision Express over Specsavers, but that probably varies with the branch.