Speaker impedance of 8 ohms suggests home hifi use though the stated performance is typical of a bookshelf speaker, designed to be at the "reasonable" end of the market - reasonable performance, reasonable quality, reasonable cost and suitable for a wide range of volume settings at the lower end of the scale...
Constructor catalogues generally offer a wide range of loudspeaker drive units including tweeters and mostly provide pictures. If you want to avoid modifying anything simply choose one that looks like yours and then check the description fits.
The speakers consist of an induction coil, and a magnet attached to the cone. You have damaged something internally or the cone itself. Speakers don't have fuses unless they are powered speakers with mains input and an amplifier. You need the speaker repaired or replaced.
Contact the maker
https://www.tannoy.com/service.html
Specs
https://www.ebay.com/p/78039939
..
If the company say they are no longer made, then it's unlikely you will find replacements in any electrical parts supplier.
If you still want to use the unit then you will have to look around for one on places like e-bay, which might be faulty elsewhere , but have a working tweeter.
A search on e-bay itself might even reveal a spare tweeter! Or a second hand that's cheap to replace the one you have. At least you will another set of spares (except tweeter of course) for the new one!
I would say from your description that the tweeters are blown.
Can you take the speaker that sounds good and swap it out with one that sounds bad. If you do that and the good one still sounds good. You have a tweeter problem. And they would need to be replaced.