The National Asthma Campaign manifesto states that people with asthma have the right to expect to be seen by a specialist whenever necessary. For adults, the specialist is usually a consultant in respiratory medicine.
Consultants work in teams, with senior registrars, registrars and senior house officers. Although any of these doctors may see you in the outpatients clinic, they work under the authority of the consultant.
Children should be seen by a consultant pediatrician with a special interest and expertise in asthma treatment.
If you and your doctor are together controlling your asthma, then referral to a specialist may not be necessary. If you feel it is necessary, you can ask your doctor to refer you, but you have no legal right to insist on this. Talk to your doctor about any worries that you might have.