Peter Costello is by far the desired Liberal leader, preferred by 56pc of voters against Brendan Nelson, in an Age/Nielsen poll that also sees a big plunge in Dr Nelson's approval, putting further pressure on the Opposition.

Mr Costello has more than double Dr Nelson's 27pc support in a head-to-head contest.

In a three-way contest, Mr Costello — who has yet to declare his future — scores 44pc, to Malcolm Turnbull's 27pc and Dr Nelson's 17pc.

The poll has mixed news for Mr Turnbull.

In a straight contest with Mr Costello, he is badly behind (35pc-49pc).

But in a head-to-head with Dr Nelson, he has an overwhelming lead (47pc-31pc).

This would put Mr Turnbull in a good position if Mr Costello carried through his earlier indications that he will depart politics — but badly placed if the former treasurer changes his mind and stays.

The latest support for Mr Costello comes as Dr Nelson's approval fell five points to 31pc.

His disapproval has risen seven point to 53pc in the national poll of 1400 people taken between Thursday and Saturday.

This is the first time a majority of voters has disapproved of him as Opposition Leader.

Since the last poll, Dr Nelson had a major setback when he was forced to retreat, amid bad publicity, from his push to toughen the Opposition's climate change policy.

Kevin Rudd leads Dr Nelson as preferred prime minister, 65pc (steady) to 19pc (down one).

But Mr Rudd's approval has fallen six points to 60pc— his lowest rating as Prime Minister although still very high.

His disapproval has risen four points to 31pc.