Is it normal for a washing machine to shock you without grounding?
Well, don't be confused by what happens in North America.  There, some very silly things were done to dryers regarding bootlegging ground off neutral, and so dryers are a holy terror.  Not Your Problem.
Your washer hooks up just like a normal appliance - Hot, Neutral and Earth.
I suspect the root of your problem is this &quot;improvised&quot; electrical connection.  The first thing you did - that is a cardinal sin in Britain and European influenced areas - is you attached an appliance to a lighting circuit.  Many lighting circuits are some piddly small ampacity like 3 or 6 amps.  They are simply not intended for a large appliance.  Only lighting can be on those circuits.   It's possible that light was herky-jerked off an appliance circuit, but you should have investigated that.
Further, it's likely the lighting cord that was run for it, was &quot;lighting-sized&quot;. So too small to run a large appliance like a washer.  Again, in Europe, never convert a lighting outlet to an appliance outlet!
Generally anytime you find hork-a-dork wiring like that, you need to go through it &quot;with a fine-tooth comb&quot;. Think about it -- when you're looking right at several Code violations, it would be insane to assume the rest of it was done safely to Code.
What you really need to do is find out whether DIY is allowed in your country, and either properly install a receptacle outlet in the room off an appliance circuit, or wire a dedicated circuit (that's Code in El NEC countries like Panama and the USA), or have a professional do it if local Code requires that.