If you are referred for your first outpatient appointment then in most cases you have the right to choose which hospital in England to go to. This will include many private and NHS hospitals that provide services to the NHS.
You are also able to choose which consultant-led team will be in charge of your treatment, as long as that team provides the treatment you require.
Therefore, if you wish to be treated by a particular consultant for a procedure, you can choose to have your first outpatient appointment at the hospital where the consultant works, and to be treated by that consultant's team – but this doesn't necessarily mean you'll be seen by the consultant themselves.
This choice is a legal right, if you are not offered a choice at the point of referral, ask your doctor why and say that you wish to go through your options. If you are still not offered, or refused, a choice, contact your local Clinical Commission Group.