Off the top of my head, Colin Campbell I mentioned already (Napoleonic War, Crimea, and Indian Mutiny) went from gentleman volunteer to FM; Hector MacDonald of the Gordon Highlanders (2nd Afghan, 1st & 2nd Boer Wars, both Sudan campaigns), and Luke O'Connor of the 23rd RWF (Crimea - first Army recipient of the VC), both made it from private to M-Gen.

More recently, Fitzroy MacLean, Enoch Powell, and a few others (Peter Young perhaps?) made it from private to B-G during WW2; Powell joined as a private as he would have had to wait longer if he had wanted to join as an officer.

Richard Vincent joined the Army as a private just post-WW2 and rose to FM, but was "spotted early" and sent to Mons OTS without passing through all intervening ranks, unlike Robertson (although I think that there were fewer WO ranks pre-WW1); Peter de la Billiere also joined as a private and made it to general.

Technically, I think all modern officers start off as a private when they enter Sandhurst, but I suspect that's not what you're talking about here.