It is arguable whether the BEF made much difference in itself, the real threat from Britain was a long war based on using the Royal Navy to blockade.
Irrelevant since the German Army planners didn't see it that way. And they were correct; the expansion of the French and Russian
(and British) armies in the 1910s meant that the campaign in the West was going to hinge on a few divisions in the right
place and the right time.
However, Britain on its own could do little to deter Germany in either WW1 or 2.
Not responding in a panicky manner to Germany's naval expansion would have helped.
Not double dealing with the French in secret while negotiating with the Germans openly would have helped.
Not appeasing Russia after being defeated in the "Great Game" would have helped.
Britain relied on the French Army to take the brunt of detering and then fighting Germany.
Britain began to institute an Army expansion after 1906. This is plainly evident in the dominions.
Naturally, the nature of cross-channel troop movement would mean that the French Army would take
the initial brunt of fighting the Germans.
But the Anglo-French were convinced that the "Russian Steamroller" would do most of the work.
That's why the Anglo-Russian accords called from simultaneous offensives within (IIRC)
two weeks of mobilization.
After 1870 this seems to have been optimistic at best.
In both wars Germany was only defeated by the involvement of the United States.
That's being wise after the fact; the Entente miscalculated horribly.
But the US was uninterested in doing anything to deter Germany before the wars.
Britain's disastrous Irish and German policies alienating the huge Irish-German
immigrant population in the US might have had something to do with that pre WW1.
In WW2, Britain's default on her WW1 loans coupled with her territorial expansion
at the expense of the defeating Central Powers, Naval expansion tension with the US, the Anglo-Japanese alliance...
Could the British have stood aside and leave the French and Germans to fight as in 1870?
Germany made this impossible by building its High Seas Fleet to challenge the Royal Navy.
But the British weren't threatened by Russian, American, Japanese, French, Austro-Hungarian, and Italian
naval expansion during the period?
Plus, the British *won* the naval race by 1912 when the Russo-French army expansion had compelled
the Germans to abandon naval expansion in order to expand the Army; about the only noteworthy
German army expansion of the period.
The German threat to the Royal Navy was in the Ottoman-German alliance and its threat to
Britain's middle eastern oil on which the Royal Navy was increasingly dependent.