I don't know how many of the POR kits Frost sells. However, if they sell the motorcycle tank lining kit, that is what you want for a Mini. The kit will come with Marine Clean ( a very strong caustic cleaner), Metal Ready (a refined phosphoric acid) and the POR tank coating material.
By all means, use the nuts and vinegar first. Get as much of the grunge out of the tank as you can before working with the small quantity of cleaner and acid that come with the POR kit. Nuts, bolts, lengths of chain, even gravel... all work to help you knock the crud off the inside. Just like any other painting project, your results will depend on the amount of prep work you do and how closely you follow the directions. Spend a lot of time on the prep work and you will have good results.
Don't worry about that pickup tube screen. Use a long steel rod through the filler neck (and a hammer) to drive the filter off the end of the tube. When you are ready to put the POR sealer in the tank, take a large diameter piece of vinyl insulated electrical wire, smear it with Vaseline, and insert it in the pickup tube until you can see it enter the tank. After the POR coating cures, pull the wire out. To protect your fuel pump in the future, install a coarse filter between the tank and the pump intake port.
I have lined three tanks using different products each time. I prefer the POR kit. The chemicals are not as nasty, the process went well, and the end result is you have a tank that still looks "metallic" on the inside. Other kits typically use a white coating material that looks out of place and discolors quickly with exposure to gasoline.
All that being said... why not get a new/used tank? Being in the U.K. you should have access to a lot of good used parts that were not available to me when I chose to line tanks.