There are auctions where that is not impossible. Very, very unlikely but not totally impossible. But running and road legal? Very, very much doubt it. More like £500 for bargain moped/scooter
I suggest you save up more than that, you will get nothing road worthy at that price and if that is all you can afford then you can afford to be on the road as you are putting not only yourself but everyone else at risk
Impossible. You would be hard to find a bike for that price, let alone anything with an engine.
You can get an "addis" from B&Q for a about £14.99
what would you recommend?