The Alternative Vote (AV) system in Australia produced a hung parliament in their recent election, whilst first-past-the-post (in contrast to the UK election) would have resulted in a clear Conservative victory.
AV changes voter and Party behaviour. In the UK the Liberal Democrats would expect to win a lot of second preference votes under an AV system but AV can also encourage votes for other parties such as the Greens (now the third force in Australian politics with Labour owing 8 of its 70 or so seats to the second preferences of Green voters). This is because such voters have the luxury under AV of significantly reducing the possibility of a wasted vote by e.g. choosing a Green candidate first and a mainstream party as their second choice. The main parties also have more flexibility to move towards the centre e.g. the Conservatives could be more confident of securing most right wing second preferences and can compete more actively for the middle political ground. Similarly, Labour could count on being the second choice of e.g. left wing Liberal Democrat voters, as it targets voters in the centre.
Overall, therefore, although AV could still favour the Liberal Democrats in the UK, the party might also find itself pushed further from the centre ground by both Labour and the Conservatives, opening up the fracture between its right and left wings.