Excellent suggestions, (((( Obayan ))))!

I think the Doctor would make an excellent Prime Minister of the United Kingdom! ( Even though he seems to rub up the British Monarchy the wrong way...Queen Victoria knighted him for saving her life, and then banished him from the British Empire. Although, that was something of a misunderstanding...

And Queen Elizabeth I tried to have him killed, so he had to make a swift exit, after saving William Shakespeare's life...Although, again, this was apparently due to a misunderstanding between the Doctor and Queen Elizabeth I on a previous visit of his...

)
And if the Cookie-Monster was head of the British state, then the Cookie-Monster would have to preside over the State Opening of Parliament!
I can see it now...the magnificient State Carriage arrives at Westminister, and the Cookie-Monster gets out to the cheers of the crowd waving their Union Jacks, and he enters the Palace of Westminster, leaving a trail of biscuit crumbs along the red carpet.
And, inside Parliament he reads the government's legislative programme for the Parliament ahead...
Cookie-Monster settles himself in his chair. An expectant hush falls over the assembled members of the House of Commons and House of Lords, as Cookie-Monster starts to speak...
" Over the coming Parliament me government will...Cookie! Yumm, mhm..Cookie!...Me love cookies...! "