The Royal Army performed very very well against Third World forces in the late twentieth century around the world (Kitchener of Khartoum, K of K, for example). But beginning with the Boer War I think its leadership was exposed as sclerotic, hidebound, and either unable or unwilling to adapt to new developing tactics and technologies. And In World War I that cost many many Commonwealth lives.
...late twentieth century...
Blame spellcheck!
There is no ‘Royal Army’. There is the Royal Air Force and the Royal Navy but the Army serves only by the permission of Parliament and its right to exist has to be renewed every five years due to the Glorious Revolution and the suspicion of the Crown possessing standing armies.
There are various regiments and corps that have the ‘Royal’ prefix in front of them though.