The guitar you choose depends on the artists and style of blues that you like.
I use a strat (well, a Carvin strat style guitar, 3 single coils and a wilkinson bridge) mainly because the artists I'm into are people like Rory Gallagher, Stevie Ray Vaughan, Eric Johnson, John Mayer (even though most of his stuff is less Blues, more pop) etc, as well as other genre's artists that use strats.
However I'd expect a Gary Moore fan to lean towards a Les Paul, or a BB King fan to lean towards a Gibson hollowbody, so on and so on.
But for a "moving up"/intermediate guitarist I'd heavily suggest something real versatile.
If you have a low budget (£100-£300) I'd suggest:
Fender standard Strat (Or high end Squier strat if you're low on cash)
Fender standard Tele (or high end squier if low on cash)
Epiphone Les Paul (custom if you have the money ;))
For a mid budget (£300-£600):
Fender Highway One Strat/Tele (or go used and find american.)
Gibson Les Paul Studio
Or copies which have a similar quality (Like I said earlier, I use a Carvin strat, got it for £600, plays beautifully)
For a higher budget (£600-£1500)
Try the higher end strats, teles, or other Fender guitars.
Standard Les Pauls or SGs (SGs are probably better for the rawer heavier stuff.)
And if you look right you could probably go custom.
Anything above that price range is just indulgance ;)
Hope I helped.