The Reichstag didn't have power over foreign affairs; appointments in the military, foreign office and for the position of Chancellor were the right of the Kaiser. Plus, Bethmann-Hollweg and the General Staff were able to frame Russia's mobilization in such a way as to make Germany's declarations of war and mobilization appear defensive, thus securing the support of the SPD (the Social Democrats) for war credits.

As for Britain, both Parliament and the Cabinet were divided over the issue of intervention, prior to the invasion of Belgium that is. Edward Grey's efforts at a peaceful solution via the Concert of Europe were torpedoed by Austria-Hungary's attack on Serbia and Germany's declarations of war. With the German invasion of Belgium, Britain was not only obligated by Treaty to come to Belgium's aid, but was faced with a serious threat to the Balance of Power and to British interests and security.

You seem to be holding to a common but hardly correct view of the First World War, that it was a scrap between monarchs in which millions died uselessly. Really, this is true only for Germany, and then only to a degree: the Reichstag had very little power in comparison to the British Parliament. The Chancellor was not a member of it, nor were ministers responsible to it. The immediate demands of policy making were effectively driven by a coterie of favourites and military officers surrounding the Kaiser, which explains a great deal of German decision-making in the lead-up to the First World War.

Germany decided on unconditional support for Austria-Hungary in pursuing its Balkan policy in December 1912, when the First Balkan War was raging and Germany regarded the Balkan League as a Russian proxy to extend its influence in the region. Considering that Austria was Germany's only likely ally in a clash with the Franco-Russian alliance, Germany's policy makes a degree of sense, but its execution was needlessly belligerent. After Franz Ferdinand's assassination on June 29th, 1914 by a conspiracy of Serb nationalists, Kaiser Wilhelm reiterated Germany's support to the Austrian minister in Berlin, the Graf von Hoyos (an action often referred to as "the Blank Cheque").

On July 23rd, Austria presented a stunning ultimatum to Serbia. The ten terms, calling for the suppression of all anti-Austrian publications and the trial of the conspirators with Austro-Hungarian observers, were such an assault upon Serbian sovereignty that it was impossible for the Serbian government to fulfil them all, though their response went far further than any observing diplomats thought possible, agreeing to eight of Austria's demands. With German backing guaranteed, Austria rejected Serbia's response. Serbia mobilised on July 25th. Austria mobilised on the 26th and declared war on Serbia on July 28th.

After Austria declared war on Serbia, the deciding power was the Russian Empire. It could not afford to stand by and acquiesce to Serbia being conquered by Austria: too much of its foreign policy credibility was built on its portrayal as the protector of the Slavs, and in any case it viewed the Slavic areas of the Balkans as being within the Russian sphere of influence. The Russian Army ordered partial mobilisation on July 29th, and then general mobilisation against Austria on July 30th. Throughout this period, Tsar Nicholas II made several personal offers to Kaiser Wilhelm to help de-escalate the situation (the so-called "Willy-Nicky telegrams"). They were all ignored. So to were proposals by the British Foreign Secretary, Sir Edward Grey, for a peace conference. On July 31st, Germany issued an ultimatum to Russia demanding that they demobilise. Of course there was no prospect of demobilisation, and Germany had to know this. The longer they allowed Russia to mobilise was less time for Germany to defeat France before the "Russian steamroller" could bear down on East Prussia. Making it appear that Russia had mobilised first was what tipped the Reichstag, in which the dominant party were the decidedly-moderate Social Democrats, to vote for war credits. The prospect of "Slavic hordes" spilling into Germany from the east was what cinched the decision. General mobilisation was ordered and Germany declared war on Russia on August 1st.

International treaties required that France intervene in support of Russia. Though the Kaiser vainly hoped that he could perhaps encourage France to remain neutral, the German Army in particular was determined to see the Schlieffen Plan implemented in full. As if to ensure that the possibility of France considering neutrality was fully eliminated, the Germans demanded that France surrender its border fortresses "as a gesture of sincerity", if Germany was to accept her neutrality. This transparent attempt to compromise France's security as preparation for a future war was of course ignored by France. Germany declared war on France on August 3rd.

The German war plan, often called the Schlieffen Plan, envisioned a great sweep through neutral Belgium to outflank the French armies massing on the frontier and encircle Paris. There was the strong possibility, however, of this bringing Britain into the war on the side of France in defence of Belgian neutrality and the Channel ports.

Despite this, Britain's Liberal government in August 1914 was extremely reluctant to go to war: there was no enthusiasm for war within the Liberal Party, and even the Cabinet was divided on the matter. Though the Prime Minister, Herbert Asquith, and other political heavyweights like Winston Churchill and David Lloyd George were prepared to fight alongside France, there was no possibility of them carrying the Cabinet, let alone Parliament: Until Belgian neutrality was violated, it utterly refused to countenance war. Even after the British government knew that Belgian soil had been violated by Germany, its final ultimatum on August 4th asked only for German troops to vacate Belgium, and Britain would stay neutral. In the event, the Germans refused, and at midnight on August 4th, Britain was at war with Germany. Even then, anti-war feeling made itself felt: two radical ministers resigned over the decision. For most of the British Parliament, however, the German invasion of Belgium made their minds up. Britain's continental policy was built on maintaining the balance of power in Europe, in particular maintaining the neutrality of the Scheldt estuary that was the Gateway to Europe for Britain's trade, as well as a gun barrel pointed at the mouth of the Thames if it fell under the control of a hostile power. This threat to Britain's naval and commercial supremacy at sea was what forced Parliament's hand.

In conclusion, it is inaccurate and arguably dangerous to believe that war could have been prevented by the good sense of elected politicians and they were only drummed into it by the conspiracies of monarchs. You can only really make that argument for Germany, and then only to a degree. The British Parliament was in a much more difficult position, where the alternative to war was a neutrality that would deeply compromise Britain's economic and international position.

Sources:

Gordon Corrigan, Mud, Blood and Poppycock

Saul David, 100 Days to Victory

Max Hastings, Catastrophe: Europe Goes to War, 1914

John Keegan, The First World War

Simkins, Jukes and Hickey, The First World War: The War to End all Wars

Barbara Tuchman, The Guns of August

Hew Strachan, The First World War, Volume 1: To Arms