Hi,
Not sure if you’ve had any luck with trying to find an answer to this. My understanding is that there are only 3 airworthy 2 seater Spitfires in the UK and getting to fly in one will prove tricky due to CAA regulations. I was looking for something similar last year.
An alternative might be to get a flight in an aircraft which flies alongside the Spitfire whilst it undertakes a number of manoeuvres. There are a couple of companies offering this
www.historic-flying-aces.co.uk and
www.goactionstations.co.uk. They might be able to help.
Good luck!