You can use as small a burner as you want as long as you 1) limit heat losses to the atmosphere (including steam) and 2) are patient. There is only so much you can do about #1 (unless you design some crazy-efficient burner), so your choices are waiting vs burner cost. You won't use appreciably more fuel to boil with a bigger burner, all other things equal.
It takes 1 btu/lb to raise water (or as a first approximation, relatively low-concentration wort) 1 F. Water weighs 8.3 lb/gal. So to bring your 14 gallons of water from 70 F to 212 F (close to the boiling point--this depends on dissolved solids) would be 14 x 8.3 x (212 - 70) = 16500 btu's. If you get all of the heat into the water (which you don't!) it will take a 55kbtu/hr burner a mere 0.3 hours (18 minutes).
Since the efficiency of the burner for getting heat into the water is probably < 50% (33%?), *and* the pot loses heat to the room, it's going to take three times that long (or worse). Keeping the lid on to minimize evaporation will help, if you want that.
Once the water/wort is boiling, the heat of vaporization is 1000 btu/lb (nominally). I can't tell you how much boiling is required to keep the water moving, but you can estimate how fast you will boil off the water from the burner size. The example burner of 55kbtu/hr @ 33% would boil 18 lb/hr (2.2 gallons) at full firing.
As I'm a card-carrying member of the International Association of Pedants, I will point out some flaws in this argument before someone else does:
1) wort will boil at a higher temperature because of dissolved solids, increasing heating needs
2) the heat of vaporization will increase as the wort boils (one reason that it's harder to evaporate the last lb of water than the first)
3) altitude and barometric pressure will matter
My response to these points is RDWHAHB. Assuming beer behaves like water is close enough.
Hm, now that I think about it, I should figure out how much beer I could make with the 350 million btu/hr boiler at work...
Edit: I find it ironic that an American answers an Englishman's question about *British* thermal units (no offense intended, of course).