They will if it's an unprovoked attack - as it was in 1866 - especially as Bismarck's regime was much disliked by liberal opinion.
Anyway, if the King, in peacetime, decides to station some British troops in Hanover, what can Parliament do, short of voting down the entire Army budget, which is hardly likely over such a minor matter? If those troops come under Prussian attack, the mob will be screaming for war, whatever they think of Hanover[1]. Such an attack would be an unforgiveable slap in the face.
And even before 1866 there could be butterflies flitting around. Will George V support the Austrian Reform plan in 1863 (iirc Queen Victoria approved of it, though the OTL King of Hanover wasn't keen) and if so could he persuade the King of Prussia to go to Frankfurt? Also, a GB still united to Hanover might find it harder to stay out of the Danish War. Even if he does, he will more than likely support the Augustenburg claims in Schleswig-Holstein.
Even if things go as OTL until 1866, they could be different then. Will King Wilhelm consent to war with Austria (even OTL he took quite a lot of persuading) if he may face an Anglo-Hanoverian "Second Front" in the northwest? If he does, he will need much heavier forces in that quarter, so the invasion of Bohemia will be quite a bit weaker. This gets interesting.
[1] British public opinion was notoriously temperamental. In 1877, Gladstone was cheered to the echo as he denounced the Bulgarian Horrors and called for the Turks to be ejected bag and baggage. By the following year, the gallant defence of Plevna had turned emotions round, and the anger was directed at the Russian bully. Gladstone failed to catch the change of mood in time, and as a result all his windows were smashed by a patriotic mob.