The Conservative party is well noted for having two wings.
There is a paternalistic, aristocratic wing that holds sway at the top of the party (Cameron, Osborne, IDS, the Tory Lords etc), and there is a dynamic small-state, free-enterprise, and generally more libertarian wing (characterised by the likes of Douglas Carswell, John Redwood). It is notable that William Hague started way over to the libertarian side, but has shifted over time so is now solidly on the other wing of the party with the grandees.
These groups have been forced together because under FPTP a split between them would result in Labour holding power for ever more - the Conservative party is already a coalition of disparate forces, the current coalition government is just a widening of that compromise.
However as the conservative compromise is extended on the left (towards the LibDems) it is straining heavily on the right - the small-state, free-market, EU-Sceptics are being marginalised more and more and are getting less and less comfortable with it.
However, under AV, voting is not so crude as to allow vote splitting to 'let in' an unwanted party/candidate. Under AV it would be perfectly possible for the conservative party to split into its two natural constituents, allowing voters to prioritise paternalism against liberty without the risk of 'letting in' a far more left wing alternative candidate.
AV will free the Conservative party to split with out damaging the right of centre political postion - this will be good for voters (who will have a finer grained choice of candidates to prefer), but will be bad for the current Conservative party grandees, and hierarchy - who put their loyalty to an arbitrary organisation above freedom and democracy in the UK.
AV will destroy the Conservative Party, but completely renew a more powerful right of centre movement in the UK. Bad for the party but good for the principles it claims to support.