Do these hot water tanks need extra insulation?

I guess with something like https://www.screwfix.eu/hot-water-cylinder-jacket-18-x-48.html

The yellow foam is not as thick as on current versions. I have a more modern one, and I put two red jackets on it because I had them from the old cylinder. They are very effective, and the airing cupboard is hardly warm now. Occasionally you can get discounts on insulation if there is an energy-saving campaign on. Check prices in places like Wilko and Ebay as well as DIY sheds. The usual brand is Manders.

I see you've done your pipes too, which is important. Pay extra attention to bends and elbows which may get exposed as the insulation pulls away. You can mitre the lagging and tape the joints tightly. If you pinch the lagging you will spot the difference between cheap flimsy stuff and the stiffer better grades.

looks like it's in a loft , build a frame around it , make a box around it with some thin plywood , then fill it with loft insulation , screw it together so you can remove it to work on cylinder , maybe a small cover for using air vent. might be a bit of work but will save you in the long run.