Hi Elaine,
The Osaka-Tokyo Hokuriku Arch Pass seems like the best fit for you. It lets you travel to 4/5 of your locations for less than half the price of a regular 7-day JR Pass.
You can purchase it here: https://www.jrpass.com/regional-passes/osaka-tokyo-hokuriku-arch-pass#regional_pass_type
Please note that this is a 7-day pass, and your trip is 10 days. From Nagoya to Kyoto, you'll have to purchase an individual one-way rail ticket, which can vary from 4500-6000 JPY, or roughly 25-33 GBP. Therefore, to save as much as possible, you can activate your pass when in Kyoto after you've left Nagoya, so that the pass is valid for the rest of your trip, and can be used in Kyoto, Kobe, Nara and Osaka.
Hope this helps! If you have any further questions don't hesitate to ask.