As stated above the Privy Council does have one very powerful role - they have to approve the accession to the throne by a new sovereign. Tony Benn, who is also a Privy Councillor has said in the past he intends to veto the accession of Chaz to the throne (providing he outlives the Queen) and so set the UK on the road to becoming a republic.

Hooray! Long live Tony Benn!