The number quoted by Ludendorff was an extra 300,000 men. In the end the army was increased by 135,000 just before the war as a compromise between increasing the army's size and retaining it's character.
The UK and Germany where in a cold war since the 1860's and certainly after the Franco Prussian war... even without a battlefleet, it was still in the UK's interest to oppose German continental hedgemoney and an alliance with France was logical component of such a strategy