My personal experience of Saga is the exact opposite. We also own a Mazda MX5. It is commonplace on these cars to increase the tyre size slightly, to get a greater choice. I told the Saga call-centre about this, she checked and came back to me and said it was not a problem. It's on my insurance that my car has increased tyre size, and there was no mention of an extra charge.
As a matter of interest, Saga offered the most competitive premium for our Mazda, but were miles out on the Lexus! Our CT200 is insured with LV, £50+ lower premium than Saga.
I hope this helps,
Brian.