To what extent has the Prime Minister become presidential?

You could mention Brown's current intention to move perogative powers from the PM to PArliament. Perhaps showing that the position has become Presidential, and is being rectified. (Current stuff = lovely lovely marks)

A president is elected by the people - the PM is appointed by the Queen.

The PM is not repsonsible for enacting laws. Interestingly enough the powers don't lie with the Prime Minister they lie with the Queen she just doesnt use them. The office of PM is a stranger to the law ie he is no different to any other minister of state exercising deligated decision making and perogative powers.

And the PM is appointed by the queen. But she will always choose the leader of the party that wins the general election.

Actually, she tried to call a minority gov in th 1970s

Hmm....difficult. It could be argued, but it would be a tad tenuous, as it wouldn't be shared per se. The power would still rest with cabinet just a more diverse cabinet. It could however be argued that his wanting of differing opinions means that he wants to listen to different opinions. As a consequence cabinet is a fully functioning cabinet not one that pander to the whim of the PM Ref Thatcher and Blair. It doesn't however mean that Brown has to act on what's said. Seemingly he still likes to be controlling, not least with the economy, so to that extent it still seems like an EXOP!

It's an interesting point though. If you can explore it it may be worth going down in the exam, it will be fairly original. The list you gave first will of course be the same list that every othr student is using(!) It was the one I used

However, the presidency point therefore fails. The powers can be taken back at any time by the monarch.

Tried to? Does this mean she was unsuccessful?

Not really, or indeed at all. There is theoretically the power for the Queen to do this, but as has been said it simply would not happen. It is even possible to argue that it would be unconstitutional.

Yeah it was pretty standard stuff. I think I need to explore as many up to date points as I can. That's what gets As so I'm told.

I'd love to see you try and argue that a monarchy with an uncodified consititution gauruntees its citizens that their head of state won't exerise her legal rights.

The point fails becaue quite simply put the de jure/de facto dichotomy prevents a true presidency ever happening here. At best you may aruge elective dictatorship but not presidency. The PM doesn't exercise even the basic functions of a president for example he is not the head of state, he is not able to sign bills in to law, he is not the head of the armed forces nor the civil defences forces...