How much does it cost to repair the heat shield under the car in England?

The heat shield you have now is fine, it just needs to be attached to something more solidly. You can buy any diameter stainless steel worm drive band clamps you need. Smaller diameter from the auto parts store and the big 8 inch diameter from a home improvement center that sells them for plumbing pipe purposes. In addition, you can daisy chain them together easily. Then you simply feed them around the catalytic converter or exhaust pipe that they attach to and clamp them in place. Any independent garage should be able to fix the shields in place with no problem. Welding is not a solution here. Basically you need what the first guy did with the wire, except with the stainless steel band clamps for a permanent solution. Even a new heat shield would just have metal tabs that the band clamps would go around to hold the shield to the converter or muffler or pipe etc.