Where to start (leaking dishwasher)?

New flat. Had a knock on the door this morning from our neighbour telling us water was coming into his kitchen.

Pulled out skirting and discovered the dishwasher was leaking (from the bottom of the unit, not the pipes). Pulled everything out to discover it's Ikea plumbing under the sink, which people appear to hate.

The building is very, very old, and we've had some issues with the sink not draining very fast. Is the plumbing the problem, or is it the dishwasher?

Was gonna call a professional but I don't know if it's a dishwasher issues or a plumbing issue or an outside pipe issue, or all of the above.

Any thoughts greatly appreciated