Difficult, since German and British interests before the Great War are contradictory. The UK does not want any power to have a hegoemony over all of Western Europe; Germany wants exactly that.
Not really...
Like has been pointed our ealier in the thread, the Great War analysed as the Great War was the result of a system of alliences that once it kicked off brought all the power-that-be into a conflaguration of war.
If we look at Germany through the late 1800s it very much didn't want war with France and Russia and even signed an allience with Russia to help prevent this. As things go, the Kaiser Wilhem didn't renew the Allience, which ended up allowing France to sign the Russo-Franco Alience (1890), and it was only as late as 1904 when Britian joined the Allience to make it the Entente Allience.
What can be seen as a major contributing factor to the hostilities was Germany's wish to challenge the Royal navy thus leading to the naval arms race between 1909 and the beginning of the Great War.
This is inself corresponds to a tension between GB and Imperial Germany, but if a suitable detente is formed anywhere in that period to 'align' Anglo-German relations in naval power, then you defuse the Anglo-German tensions.
Indeed, if Germany doesn't mobilise offensively against France and instead mobilised to border regions and only joins with Austria-Hungary against actions against Serbia and Russia, once Serbia capitualates the triple allience can sue for peace.
A peace that would likely be accepted by the French, but not by the Russians leading to a fragmentation of the Entente Powers.
Britian never gets involved because the German millitary doesn't threaten the Low Countries.
Counterpoint: The French and English were in talks through the late 1900s about Germany's industrilisation, but in the context of things one has to realise this is the legitermate 'jelosity' of France and Britian against accepting a new Great Power in Europe, and bugger all to do with German 'warmongering' if anything its the French beginning these talks and alliences that could be considered the 'warmongering', since the Russo-French Allience is designed to counter Germany specifically.
From the English point of view, it is the fate of France that nessitates their action.
What the British fear is that a repeat of the Franco-Prussian war will lead to France becoming 'annexed' or 'controlled' by Germany, and hence giving Germany access to the Channel and the Atlantic. This coupled with Germany's naval build up, looks like some grand strategic plan to control Europe. Especially after Britian starts creating propaganda to that effect.
In reality Germany's naval build up is her flexing her new industrial power for her colonial ambitions as a new nation of European importance. To be an important European nation, you need to have colonies and a decent army. Which is her rationale.
Which means, if Germany during the Balkens crisis makes clear that Germany won't invade against France, but will stand by Austria-Hungary, then Britian has no 'Just Cause' to enter the war, and most likely won't because the geopolitical propaganda has just backfired on the government, and after the first few losses start rolling in by the end of 1914 its going to look dicy for the French offensives if conducted (if the French don't conduct offensives, then a late entry may be more likely).
The key points of divergence;
1. Some time during 1905-1914 Anglo-German relations reach a detente over German naval ambitions, be it treaty or simply a reduction in expenditure.
2. Germany rules against the Schlifen Plan, in favour of a defensive stratergy against France. (This could be the result of Austria-Hungarian-German communications being simply better; since the AHs wanted help against Russia, not France and France was only being dragged in by relations ostentaibly; although see counterpoint)
3. Germany makes clear that she is only supporting Austria-Hungaries position in the Balkens, and against Russian influence and has no 'quarrel' with France. Which to some degree Germany didn't, sure there was bitterness between the nations, but there were not any large claims Germany could make on French territory in Europe or fessibly any way to control the entire french nation.
These points are not extensive, but they do require the change of focus, over changes in inderviduals. Therefore it is unlikely to occur, unless you can create some POD that creates a change in the
zeitgeist of the time PPPN.