I had a similar situation at home: an old washing machine, and as soon as I turned on the hot water - click, and all the lights go out. Turned out it was a combination of several factors at once. Old wiring often isn't designed for the power draw of modern appliances, especially when they heat water. Plus the washing machine itself might have insulation problems with the heating element - microcracks in the cable or corrosion that's built up over the years. An RCD catches even tiny current leaks to the chassis, so it trips almost instantly.
Here's how you can check: run the machine without heating the water - if everything works fine, the problem is definitely with the heater or the cable powering it. If it trips anyway, then it's a broader wiring issue. Old apartments often suffer from oxidized contacts, thin wires, and missing proper grounding, which is essential for an RCD to work.
The solution depends on what's actually causing it. If it's the machine - you need a technician to diagnose it or maybe replace the heating element. If it's the wiring - you can't avoid calling an electrician; you might need at least a new breaker and RCD that are more modern, or in the worst case a partial rewiring of the electrical system. Don't just try increasing the breaker rating hoping it'll help - that's dangerous.