A full copy of the current British Army dress regulations can be found here. It's a 1,279 page PDF. Obviously, it is not obeyed scrupulously all the time, and there is a history of senior commanders dressing somewhat informally. A prime example is Lieutenant-General Thomas Picton, who commanded his division at Waterloo in civilian clothes, because his luggage had not arrived. It would not have been sensible to spend time borrowing uniform: the forthcoming battle was what mattered.
For the first photo, note that Churchill and Alan Brooke are visiting Montgomery at his own HQ. That means he is the officer ultimately responsible for dress standards, and in the field, these things can be relaxed if it does not impair efficiency. There is a legend that George S Patton insisted on saluting in combat zones; a British officer who did that would be quietly corrected by his commander, and subjected to "saluting traps" by his men.
In the second photo, Montgomery is engaging in a little image-polishing by wearing combat uniform, implying that he's achieved more than all these brilliantly-polished staff officers. However, when you look at the very short list of men who were awarded the Order of Victory, and see that he was awarded it before Eisenhower, Monty has an arguable point. He's also the senior British officer present, so there isn't anyone with authority to complain.