You’ll probably have to lengthen the chain even if you just go from a 25 to a 27, depends on how much slack there is currently. I did the Whitton a few years back as a very raw road bike rider with an 11-25 at the back and it was fine, if a little harsh on Hardknott – compact chain-set – this year I went with an 11-27 and it was, slightly, easier. I guess whether you go to a 30 depends on how strong a climber you are. I’d say I was pretty average, but my local riding in the Peak is hilly, so I guess I’m used to it,.
What I wouldn’t do is fit a larger cog at the back and reason that you won’t ever go ‘big-big’ then end up tearing your mech off in a moment of absent-mindedness.
You don’t say btw, if you’re using a compact or a standard double. If the latter, a mate of mine stuck an 11-32 XT cassette and a mtb rear mech on for the Whitton a few years back and it worked for him. Looked horrible though 🙂