Re' Melody Gardot, you might like Stacey Kent. Not exactly the same, but... well, just check her out and make up your own mind:
Also check out Rumer:
Re' Beth Gibbons, I don't have a specific suggestion for anyone similar, but, on the Portishead side of things, I highly recommend you take a listen to John Martyn's cover of 'Glorybox' - it's absolutely superb:
I used listen to Portishead, Morcheeba, and Massive Attack a lot, during my university days... memories... If you haven't heard Morcheeba or Massive Attack, you might find enough of their sound in common with Portishead's 'trip-hoppy' sound:
Axiom Funk (feat. Bootsy Collins):
Nightmares on Wax:
Re' Sarah Jaffe, you might try Julia Stone:
and, although they are male artists, you might like Ray LaMontagne:
And, of course, there's Lana Del Ray, though she seems to attract strongly polarised love/hate opinions from the listening public, so she may not be your cup of tea:
Or Paloma Faith:
If I think of any others, I'll let you know. To be honest, I didn't find it particularly easy coming up with suggestions for the 3 artists you mentioned, because all three of them have quite a unique sound.
An incredible eclectic mix of great music...Thank You!