Thermoplastics can be welded with heat. I used to use a dedicated temperature-controlled soldering iron - plastic needs to melt slowly and not bubble. Tip needs to be perfectly clean, ie no solder, to avoid inclusions.
Welding from inside would give a better chance of a watertight result.
Technique takes a little practice but you can do that on the outside at a place where the plastic is thick. A bit like stitching - push the iron 3/4 way into the crack, withdraw it & smooth the surface, repeat along the whole crack.
Avoid breathing the fumes.
Auto body shops weld plastic parts
this way if you don't want to do it yourself.
Might be able to use polythene sheet, clingfilm or similar between the cap and the opening as a temporary fix, or maybe just clean inside the tank & permanently seal around the cap until you can replace the whole tank.
I couldn't find a picture of that pattern cap on Google