ccjersey,
I'm pretty sure your original post was mostly correct; it just had a few slip-ups. Bill took issue with what you said about numbers of conductors, but you were totally correct that a service with only two conductors will always be only a single-phase service, even if it is derived from two phases on the transmission/distribution side.
For the benefit of the original poster, who was not sure what is meant by phase, it generally means a separate wire on which the alternating-voltage waveform reaches its peak at a different time. When I was still a child, I envisioned AC voltage as a square wave, but actually it is a sine wave. Look it up if you don't know the difference, and recognize that a sine wave varies continuously, repeating the same wave form 50 times per second (or 60 times over here in the USA). Because the available voltage crosses through zero 100 times each second, there is no power available from a single-phase supply at those times. Hence, a phase can be added, another wire with a voltage that varies at the same frequency, but crosses the zero point at a different time.
Years ago, there were two-phase systems with the phases 90 degrees apart. One wire would be at maximum voltage (positive or negative) while the other one was at zero. There are very few of these systems still in existence. All modern power distribution is done with three phases, evenly spaced 120 degrees apart.
Your main power line in the street has 3 hot or phase conductors and one neutral (grounded) conductor. If you take a voltage reading from phase to phase, it is 415 volts, phase to neutral it is 240. Your service should be derived from a single phase conductor and the neutral conductor, in which case it is a single-phase service. The switches on your panel board would be known as "circuits" here in the United States. If they call them "phases" there in the UK, it is technically an incorrect use of the term "phase."
And, if your house requires more power than a single phase service can provide, it would normally be done by bringing power in from all three phases, and the neutral, for a 4-wire, 3-phase service. You possibly could have a 3-wire service using only two of the phases and the neutral, but I think most people would say you couldn't really call that a two-phase service. True, if you looked at voltage to the neutral wire, you would have two separate 240 volt wires with the peak voltage occurring at different times. But it would be difficult to make use of that supply to drive a motor or piece of equipment, because the two are separated by 120 degrees, so there is no easy way to fill in the missing one that is 120 degrees separated from both. Two-phase equipment isn't built like that, so you would still only be able to run single-phase equipment from your service, although you would have two voltages to choose from, 240 or 415.
It actually is possible to derive a true three-phase service from the above-described two phases of a 3-phase system, but to do so, you have to put in a bank of two transformers, Y-connected on the primary, open-delta on the secondary, meaning there's an empty spot where the third transformer would be connected in a true delta configuration. If you do this, you have three phases available at the three corners of the open-delta, but you are still limited in total power to what your two phases can supply, and you would put an unbalanced load on the true three-phase supply that your system is derived from (because the third phase isn't being used).