How powerful was Britain's army during World War 2?

Very powerful, to give you an idea: in 1939 the army was quite small however the government introduced conscription in 1939 and by 1940 the army was far larger with 50 divisions in the UK with each division containing roughly fifteen thousand men and more than two hundred thousand soldiers stationed in India. The RAF was quite small in 1939 but the Royal Navy was by far the worlds largest and most powerful navy. 13 divisions were deployed into France as part of the British Expeditionary Force and after Dunkirk the British Army numbered 1,650,000 although only 100 tanks were left. To put this in perspective the current professional British Army numbers roughly 100,000 trained soldiers.

Prior to D-Day the army was deployed to fight across the empire from Singapore to Egypt. On D-day Britain deployed 19 divisions and contributed almost half of the total 47 divisions (USA contributed 21, Poland 1 Canada 5 and the Free French 1)

By the end of WW2 the British Army numbered 2,920,000 professional soldiers although by this point the US navy had become the most powerful in the world pushing the Royal Navy into second place.

America may have played a huge part in the allied victory of WW2 but the British certainly pulled their weight. The only nations with more powerful armed forces at the time were: America, Russia and Germany. France did start with a larger army but as they surrendered so quickly...

Hope this answers your question.