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Hornets are pretty quick, I agree with soul that you will learn more (and potentially live longer) starting off on a smaller bike. A 250 or 300 will be more than capable of meeting and exceeding many speed limit you find in the U.K.
For the other half have you considered a more modern Vespa/piaggio thing? Old Vespas are fun and nippy but things like reliability, gear change grip shift and clutch on left hand, throttle on right and pedal brake could be a challenge for a noob.
Maybe consider a sporty 250 or 300 as a first bike.
If your dad isn't that fast any more, you'll have no bother keeping up. They'll be much cheaper to buy, insure and ride and i think you learn a lot more about the physics of a bike on a lighter one like that. Plus, you can red line them all the way around town and avoid prison.