The British military was not what it would be in the 1880s, and it was a mere shadow of its former glory the Napoleonic Wars. Not only would it not have made a profound difference, it most likely would have been flattened by the Prussians.
It was small and somewhat backwards, unfortunately; the British soldier was perfect, in concert with its Navy, for the many famous actions it did abroad, but it was woefully unready to fight a European war. The Crimean War illustrated this. Not only where the British overstretched, but they showed themselves to be behind in grasping the effect of modern technology on warfare; it took insubordination by the Coldstream Guards for the British to learn what their new rifled muskets were capable of*.
Up until 1870 France was considered to have
the Army in Europe, and was mimed and studied inexhaustibly. The Franco-Prussian war would show that the French Soldier and their Junior officers were rough and ready to fight a modern war, but their logistics, General's and staff, were not. If the French, thus far considered the best in Europe, were no match for the Prussians, what would make you think the underfunded and undermanned British Army would be? There would have been a trouncing, not a stalemate.
*At the Battle of Alma (
http://en.wikipedia.org/wiki/Battle_of_Alma) the British exhausted themselves in brave but reckless charges against Russian positions. A redoubt would be taken, and promptly lost to Russian reserves. The Coldstream guards, ordered to go into the fight after having just seen the Scots Fusiliers cut to shreds, showed a rare case of insubordination when they refused. The outraged Brigadier watched as Junior officers formed the Guard into lines at 1000 yards and fired volleys. Then was quite surprised to see the Russian musket-lines get devastated in short order. It would take many more battles before the utility of the
minie rifle would become apparent to the British Army at large; and Alma sounded the death knell for the smoothbore musket -carried by the Russians even at that time.