Thanks for all the replies.

Okay.. first, apparently I need to think about gear ratios... e.g. 50/34 and 46/36; I'm going to have to look into that. I hadn't even thought about different gear ratios.

Second, what are mechanical disc brakes like vs hydraulic? I am used to hydraulic disc brakes on my Trek, but I don't think I'd be too worried if the breaks were not quite as responsive.. As long as I pull the lever and I slow down

I went to a shop yesterday. One of them was a Specialized dealer so their main interest was selling me a Specialized, but I used it to try and get an idea of the size I'd need. They guessed me at 56 due to my size, but turns out I need a 54. I must have a shorter upper body. I'm wondering now how that translates to Giant (if I went that route); I'm guessing I'd need a medium (M), not a M/L and definitely not an L! There is a second hand M for sale that's barely been used but it's a bit of a drive from me (over 100 miles...) so maybe trying some at Rutland Water would be a good idea, if they have the sort of thing I'm looking for that is.