During World War I's Battle of Jutland, the German High Seas Fleet had the objective of luring out, trapping, and then destroying a portion of the British Grand Fleet, as their numbers were insufficient to engage the entire British fleet. This was a part of Germany's strategy to reduce the Royal Navy's numerical advantage, break the British blockade of Germany and give German merchantmen access to the sea.
What would have happened had the Germans succeeded in destroying the British force? This was a very real possibility. The British lost three more ships and twice as many men as the Germans did. With different tactics and a little luck, the Germans could have pulled it off. It also might have happened on the next day. During the night, the British moved to cut the Germans off from their bases, hoping to continue the battle the next day, but the Germans slipped out under cover of darkness. If the battle had continued the next day, the British, already having sustained greater losses than the Germans, might have been defeated.
I can imagine that the Royal Navy's strength in numbers would be severely dented, but I am not sure whether even such a grievous loss would be enough to allow the Germans to break the blockade. The Germans also had heavy losses at Jutland, and with their smaller fleet, the British would probably come out on top in a war of attrition. In OTL, the loss of eleven ships probably hit them harder than the loss of fourteen ships hit the British.