@Smurfy76 I'm with bertsmobile1.
I have a Honda pressure washer that is sitting in my shed as a future project. The engine is fine while the pump (#2) never has been the same on a nice engine. I'm pretty sure it's the pump for you as he suggested a few times. I have a Suzuki pressure washer that has been behaving the past 8 years. I make extra sure to always run her with the water flowing cuz that pump has some pretty high rpms and you want that water flowing to cool the pump. I do not run any of that soap/cleaner mixture mumbo jumbo cuz that will do wonders for oxidation (rust) inside of your pump. ? So between rust and fried bearings/seals the pump is always the weakest link. I agree the replacement pump kit is basically 1/2 the cost of the pressure washer and the design is sub optimal.
So my 2 cents would be you may want to decide if your project is to get the engine working only or you really want to see if you can get her pumping and using the whole kit & kabootle.