How long can Britain last against the industrial might of the continent?
In 1900? a surprisingly long time,especially considering the British control access to rather a large proportion of key raw materials and further more of their industry is concentrated in the relevant forms of manufacturing for a naval war.
Look what Germany did to British shipping in WWI
Not terribly much save by submarine warfare which is not due to the immaturity of the technology a choice available to them here. Further but this was after 14 years of considerable build up and investment in both combatants and the infrastructure to support them.
And that is with no help and fighting three continental powers.
Actually the British only had to deploy warships against two other powers....oh you mean the Germans but the problem is on the high seas they did not even come close to challenging the British alone despite a much, much,much larger navy in both absolute and proportional terms than you see here.
Now how badly do you think British shipping would be devastated with Britain not having the French and Italian navies to help them but rather having to fight them or how the British will operate in the Mediterranean with the straits of Gibraltar cut off?
Except if you look at the numbers available in this era the Italian and French and German navies would fail to achieve the ratio of combat units to the RN the Germans achieved in 1914 and are further behind technologically on a per unit basis.
Just substitute torpedo boats for submarines.
And you find it does not work as they lack the sea keeping for the role you envisage let alone the range.
The effects are going to be the same- and the British are going to have to fight worldwide given the network of bases available to the continent
No they are not as any power that is foolish enough to raise a hand against them is going to find that hand cut off as it tries to reach out to its bases outside its own metropolitan regions. The British are the ones with the bases and the numbers everywhere you turn to look.
Just the loss of Continental trade is going to ruin the British trade
This is the only remotely true statement in your post. The issue is while British trade will definitely take a hit so will that of any of their attackers by a much greater degree...sea trade even today is the key portion of cargoes delivered. Now since the British are under attack they will be more willing to sacrifice in that regard but you are asking other nations to give up practically all their foreign trade to help Germany out of a pickle. People are somewhat inclined to be sceptical of that happening.
In fact given the nature of the conflict and the issues at stake Germany might prefer other powers not join in as that lessens the effect of the British blockade on themselves. Of course the problem for Germany one on one is that they lose a significant portion of their economy their merchant marine as a productive organ, the fees and salaries that would have been spent in Hamburg now get spent instead in Antwerp and Rotterdam and other nations get to wax their tariffs on everything that Germany would export or import and all of this on top of the fact that rail travel is more costly per tonne kilometre than sea transport.
You have all the recipe for a nice fat recession there.
Hence your need for allies for Germany (thought note not for the British) and your inability to justify why they should commit to such an action.