I think in the UK, they use the term "learning Disability" in a different way than folks in the US. Using the Federal Definitions for the United States, as well as Classification Systems for IQ tests: Learning Disability refers to a person who has normal cognitive intelligence, but has poor academic skills, generally in either reading, math, or written expression. In other words, you have to have an IQ of 85-90 and academic skills well below average to get this title (and the services that go with it). I hate when people say LD people are stupid, they aren't, and they have the IQ scores to prove it! Many people with Learning Disabilties go on to lead normal, productive lives, even though they may still have a weakness in one academic area or another. Most of us can compensate for weaknesses.
If you really mean a person who is cognitively delayed, titles for that are mentally retarded, intellectually deficient, or simply well below average- that refers to an IQ below 70, which is the bottom 2 percent. A further breakdown of this group would be mildly mentally retarded (this person can be educated to a 3-4th grade level, who will likely be able to work and support him or herself, with a little assistance), moderately mentally retarded (this person can work in a workshop, but won't be able to live independently but perhaps in a group home), to severely mentally retarded (this person will perform as an infant much of their lives and may not learn to speak or toilet independently).
School Psych who evaluates both of these types of students. For the record, my state uses the term 'Cognitively Disabled', however, for the moderately to severely delayed kids who's parents want to access government special programs, I have to also say 'moderately or severely mentally retarded' in my report for it to be accepted! They are in the dark ages.