The UK wasn't ruled by a bunch of idiots. They'd probably have declared a naval exclusion zone in the channel to both sides---i.e, anybody moving warships through here except by very limited prior arrangement constitutes an act of war. Then if the Germans violate it, they'd protest and/or declare war. French violations are more likely to get protests than war. They're unlikely to play gotcha with a charnel house of a war like WWI. They might well decide that having everyone else wreck their navies would be a good thing for the British Empire, especially if they could persuade the Germans and French to sell them some of their colonies instead of taking quite so many loans.
EWHM
Can't remember the details but pretty certain that Britain had made clear that if the HSF entered the Channel [before Britain joined the conflict] it would be considered an act of war.
However, if Germany had stayed on the defensive and mauled the French attacks, then broken through in a counter-attack without going through Belgium Britain could well have stayed neutral. There's no particular reason for the Germany to need to send their battle-fleet into the Channel.
Steve