In reply to Co1in H:
You probably know about this, but if not there is a tremendous amount of information (including, for example, GPS coordinates for all the turns on the approach) on Supertopo,
http://www.supertopo.com/rock-climbing/Yosemite-Valley-Half-Dome-Snake-Dike . Beyond that, the internet is chock full of info and videos.
The hardest climbing is 5.7, which is nowhere near UK 5a, which I think is more like 5.9. (But of course one can get off-route on the lower slabs and end up doing something harder than the official grade.)
The Dike is low-angle knobby climbing---easy, delightful, but without protection. First do a few routes in Tuolumne Meadows if you aren't used to this sort of climbing and you'll just romp up the dike.
The summit of half dome is not a place you want to be if there is any electrical activity in the area. Yosemite weather is very mild compared to alpine weather, but afternoon thunderstorms, which are not all that common, can nonetheless build quickly. This is the main reason for the early start.
There will probably be crowds on the route and will definitely will be much bigger crowds on the descent.
If you opt for a guide, it will, I think, run about $400 for one client and $500 for two.