Trackday pillion ride

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Got a big birthday coming up. Have done a trackday in my own car, and had a passenger car ride experience.
There are many experiences advertised for cars, but I would like a go on the back of a high performance motorcycle with a very capable rider.
I have never had a bike licence, and only ever been on the back of a bike once.
Any suggestions please, as can't see anything on the 'net.

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Thanks for all the replies. I'm in Northamptonshire, so fairly central, but alas it seems Silverstone don't do them as someone mentioned.
I can understand the insurance problems, and I'd need full kit supplied, and I'd doubt if I'd bounce very well either.
I suppose karting is the next best thing, and I've only done it on inside venues. I'll see if Whilton locks do it. Thanks again.

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Donbot said:

Looks like you will have to get a bike licence and a bike for your birthday instead. nudge nudge etc.

Ha, just bought an Abarth 595, which seems to be the nearest I'll get to a bike.
One review I read commented, it was as near to bike as you can get without getting cold or wet!
Took it to Whilton locks karting today as they had some racing on. Going to go on an arrive and drive soon, and I'll take my grandson to have a go in the Bambino class!
Good idea about Kimbolton. That's one of my favourite roads, so I'll go to that meet as well.
Thank you all for your suggestions.