It's not a case of attractiveness, so much.
See, OTL the idea of the Allies was to rush an army east to help the Turks. By the time both had assembled ~30,000 men, though, the Turks had already won some victories, so the Allies spent a bit of time wondering what to do with their armies and then decided to invade the Crimea and take Sevastopol - it wasn't that it was militarily important as such, a blockade with ships would suffice to prevent the Russians sallying, it was just so they didn't look like idiots.
Without France in the war, there's two effects. Firstly, the deployable manpower at short notice is pretty much halved - you get the British contingent only - and with only 30K troops invading Crimea is much less feasible. (The funny thing is that it would have worked, as far as we can tell, because the British wanted to move fast enough that they'd have taken Sevastopol before it was reinforced and the French slowed them down, while the British won all the early land victories for the most part - but that's hindsight they would not have.)
Secondly, the British are a naval power - the naval power - and so there's no expectation for them to get involved in a big land campaign like there is with France. They'd be free to handle things with naval raids, possibly in the Baltic.