Not really. The majority of the conflict took place on Europe and the involvement of outside powers linked to Britain are only limited to Japan capturing the German Islands in the Pacific.

A point that could be brought was the naval race between Germany and Great Britain. The British policy regarding the size of it's navy was based on having the next two larger navies be of equal size as theirs, this was fueled by the plan to block the German coast in case of war breaking out. When Wilhem decided that Germany needed a fleet at least 2/3 that of the British this pushed both sides into an arms race (added to the fact the US was increasing it's navy size as well). Shortly after in 1906 the HMS Dreadnought was completed, effectively making the German fleet gravely inferior and encouraging them to expand even further. The naval race slowed down when Germany, being in no position to outproduce the British decided to focus it's effort on U-boats and effectively stopped in 1912 as the Germans, weary of the Russian threat to the east, offered to accept British superiority in the seas in exchange for them to remain neutral in conflicts not directly started by Germany. The deal was rejected but it was popular among those seeking a more friendly relation with the Germans.

This is probably the closest one could get to British responsibility for the war, as Germany may have been more conservative on fueling an European crisis and it would have discouraged the other side to commit fully on a war without naval superiority, that said there was no real way for the British to predict the consequence of this decision nor it would have made sense for them to renounce the ability to act in case of war just for reasserting that they indeed had (strugglingly) maintained their naval advantage over the Germans.

The Naval race did have an interesting side effect, which was fueling the three-way naval arms race between Brazil, Argentina and Chile, though this one stopped as the supply for ships ran out when the war started. Actually, the acquirement of three Dreadnoughts by the Brazilians in comparison to the two each Chile and Argentina bought made Europeans weary of the fact the Brazilians could sell the excess ship to other European nations in order to shift the balance of power.

Christopher Clark , in his Sleepwalkers,argued that some culpability rests with the British in their July 1914 handling of negotiations between France, Germany, Russia and Belgium. Lord Grey would not clearly state exactly what Britain would do in case of a German invasion, seemed to leave room for the Germans to think that, unless both Russia and France were invaded, Britain would stay out. He and Asquith also seemed to feel that expressing strong English backing of France and Russia would make them more militant, goad them to be more provocative towards the Germans. He did not actually clearly notify the Germans that Britain would intervene to defend Belgium until July 31, when German forces were about to attack and it was too late. Lord Grey seemed to feel it important to give himself room for maneuvering, but the result was Britain's allies were not sure what it would do, and Germany thought there was a good chance it would do nothing.

Clark's argument was that there was a sort of general cloud of such missteps and mis-communications that allowed all the European powers to drift into the War. While Clark does make a good case for the British fumbling the negotiations, he has been very heavily criticized. For one thing, he pays too little attention to the pre-war history of the Germans. They had emerged as a unified power later in the 19th c., had some aspirations of expansion, and already had gotten excellent results from their use of war to achieve their aims, gaining from Denmark, France and Austria. While it's possible to argue better English diplomacy could have averted the war, it's hard to get away from the fact that the Germans were optimistic about war, ready to invade, and did invade; Grey not figuring out how to talk them out of it is regrettable, but not culpable.

The idea of making the conflict global, instead of only European, actually appealed to the Germans. They set General Lettow von Vorbeck's army in Africa to embark on a sort of long Sherman's March there, in order to drain useful British resources away from the European theater. While Lettow- Vorbeck was never able to actually capture and hold territory, he was able to move in a vast mostly undefended landscape, and did indeed tie up British forces in pursuit...while also spreading death and destruction over a big part of sub-Saharan Africa.