Is anybody legally responsible? Possibly. It would take the argument that OP is on a single ticket departing the EU and that Ethiopian cancelled, albeit a segment on a non-EU carrier between two points outside the EU. That would generate cancellation + duty of care compensation (hotel). OP could use the cancellation compensation for taxis and the like.

But, OP chose not to do that, so will not obtain anything from Ethopian and EK isn't responsible at all (not the operating carrier of the cancelled segment).

Even had OP accepted the original reroute with the three day enroute delay, it would likely have taken an action in the UK (easy enough to get Ethiopian into court) to wring anything out of them.

Best place to turn here is to travel insurance. If you make journeys such as this where multi-day reroutes are in the cards, this type of coverage is relatively cheap and very handy. It would likely have covered some flat sum without a question and that would have covered fare differences, taxis and the like.