I can't imagine any serious fighting continuing with just the British against the Germans. The UK and Empire by definition lack the manpower, production and funds of UK & Empire plus France plus America.
Not really relevant, though. Germany also lacks " the manpower, production and funds of UK & Empire plus France plus America".
We may consider war aims, capability and vulnerability.
Britain's war aims in WW I were far more pragmatic in WWI than in WW II. Pretty much the classic policy that she had followed since Tudor times: don't allow a naval power to occupy the Low Country ports. If Germany were willing to withdrawn from the Low Countries, then an accommodation should be possible. If not, Britain will fight on.
As regards capabilities, by 1918 both countries would be exhausted. But Britain, with the Dominions to draw on , and access to world markets would be in a better position than Germany . Assuming that the British troops had been evacuated (ie, France had truly capitulated, not just been partially occupied) then there would be little fighting on the Continent. We would have very much the situation of the Napoleonic Wars. Britain would not be able to field an army powerful to take on Germany. Germany would not be able to deliver her powerful army to where it could seriously hurt Britain (that "moat defensive to a house" again). The bombing capability of the day was not sufficient to be more than an irritant.
So long as the Fleet is in being, Britain is safe. So long as the Army is in being Germany is safe. They will cast about for places of combat on the periphery - like Spain in the Nap. Wars. Maybe Italy? Or another go at Turkey?
As to vulnerability, as noted above neither is vulnerable. The HSF could not take out the Grand Fleet (and Britain can reinforce it from the foreign stations). Neither country is going to be in a financial position to seriously increase naval capacity quickly (though Britain would win such a race) . "I do not say they cannot come, my Lords. merely that they cannot come by sea".
Sooner or later sensible chaps would realise the futility of such an exercise in attrition and sit down to work out a solution. The major stumbling block to that would be the extraordinary stupidity of Wilhelm II. And the extraordinary stupidity of that little Welsh git.
The only caveat in this is , what happens to the French fleet? if it is handed over intact to Germany, then the case is altered. The HSF plus the French fleet would be an interesting challenge for the Admiralty. Though personally I have no doubt that the Senior Service would come through trumps.
If the French fleet makes a bolt for the safety of a British channel port, then the stalemate is even more certain.