The deputy PM is an artificial entity created by past PMs for expediency. Eg TGL made Willie Whitelaw deputy PM. There is no succession order like in the US and no precedent in the constitution. If anything it should be the deputy leader of the party, though there is no precedent.
drmorgans: "Is there a deputy leader of the party, as opposed to deputy PM? " - yes they are two separate things, they can be different people though not in this case.