Laura,
The London AS diet, the low starch diet, aims to eliminate staple foods with high starch contents; bread, pasta, rice, potatoes, cake, and I would add pulses. All these foods have starch contents in double figures, typically 30%, and as great as 80% in the case of wheat based breakfast cereals.
The no starch diet is more radical and aims to eliminate foods with low starch contents such as banana, 1.7%. Those whose guts have been compromised by NSAIDs, or who suffer with irritable bowel disorders often find they have to resort to this.