There are a number of other high honours without title that rank above most Knighthoods - the Order of Merit, the Companion of Honour for example.
The two biggest problem with the idea of such a Knighthood I can see is that it doesn't fit particularly well into the real British traditions of Knights. Most Knights of the Middle Ages hadn't really done anything significant to earn their spurs - they were Knighted before they ever entered their first battle. The early Orders of Chivalry really described a particular job a Knight set out to do. From the establishment of The Most Noble Order of the Garter (the oldest order still in existence, dating to approximately 1350), it was awarded for both military and non-military service. There's 660 years of history behind the current system. The second problem is the issue that there are significant numbers of people who do not wish to bear a title - they do not object to decorations or honours, merely titles. Should they be denied recognition because of their beliefs?
Personally, I look at General Sir John Monash GCMG KCB VD as my image of a 'modern' (actually World War I) warrior-Knight. He was the first man in two centuries to be knighted by a British King on the field of battle.
To me that seems all the honour a true Knight needs - and the Orders of St Michael and St George, and the Bath, provided what was needed.