The law as to who goes first at an uncontrolled intersection relates to everyone giving way to their right.
This can be confusing when traffic lights have failed but all you need to do, if it is safe to enter the intersection, is give way to the right.
It’s not who gets there first or having turns at going, it’s a matter of giving way to the right. And don’t forget, you must give way to all pedestrians.
The law also states that you must approach an intersection at a speed that you can stop to avoid an accident. So it doesn’t matter who is in the right or wrong, accidents should not happen if we all approached at a speed that we can work out what is happening first, and then whether it is safe to go or stop.
If it is a ‘T’ Intersection, then you must give way to all vehicles travelling in both directions on the road you are turning onto, and also give way to all pedestrians.