Does a washing machine in the UK render Najis clothing Tahir? For example, if one had a wet dream, is it sufficient to put the Najis trousers in the washing machine (mixed with other clothes, and washing detergents, etc.)? Or if I had blood on my t-shirt, can I just wash it in a washing machine to make it Tahir? Or must I place the Najis clothing under water once to get rid of the Najasah, and then once again place it under running water (as told heRE: https://youtu.be/loEEoqc-AcM)?

You must remove the actual najasah from the clothes before washing it. Once the najasah has been removed, then you can put it in the washing machine and as the water is more than kurr it will make it purified.