This system, which we call Preferential voting, works here in Australia and usually means that the winning party receives more than 50% of the Two Party Preferred Vote across the whole country or state. If the electoral commission has done the job of adjusting electoral boundaries fairly, that is. Occasionally, one party will win with around 48% of the 2PP vote as happened in South Australia this year but that sort of outcome is nothing in comparison with the unfairness of your system in the UK where a party can win with 36% of the vote.
The advantage of preferential voting is that you know that the winning candidate is always acceptable to more that 50% of the voters in a single electorate and the winning party is usually acceptable to more than 50% of all the voters across the country.
It certainly does not favour extremist parties.
The Conservatives may worry that all of the preferences from the Liberal democrats would transfer to the Labour Party. In practice this will not happen. Probably only 60% of the vote would transfer to Labour. 40% would go the Conservatives. The vote for independents and other parties would go where the voter stipulated. Chances are that in the current election where Labour is on the nose the Conservatives would have won a significant victory using this system. Non-Labour voters are likely to preference Labour.
Based on the experience in Australia this system is far more favourable to the conservative parties than the Single Transferable vote or Hare-Clarke system which is employed in Tasmania and the ACT. In those jurisdictions it favours the Labor Party and the Greens.