I think many airlines do this - offload pax on the expectation that they won't make their connection, particularly when the next flight is busy and there are people waiting. KLM seem to do it a lot at AMS, too.

Of course it's annoying. The agent you spoke to in AUH, however, had no way of guaranteeing that your seat would not be given away in this manner. I don't think it's possible for anyone to prevent this from happening - certainly not at an outstation, anyway.

You haven't mentioned whether any compensation was offered/paid. Due to the involuntary denied boarding, you are entitled to compensation under EC261/2004 (the full €600 I believe) and they should have paid for your overnight accommodation. They are not liable for paying for your missed onward flight from EDI (it is always a risk to travel on separate tickets). Make a claim here.

I note that you said you passed through "customs" at LHR during your transfer. This is incorrect - you only clear customs at the point of arrival (which, for you, would have been EDI). At LHR, you clear immigration (passport check), only arriving passengers are subject to the full customs control.