No, not necessarily.
Apart from the consultant there are middle (registrars) and junior grade doctors (and other healthcare professionals) who will work with them. So your operation may not necessarily be done by the consultant but any member of the team.
Whoever does your operation will be suitably trained and qualified to do your operation. It may also be possible that another consultant does your operation. This is especially the case when people waiting for an operation are pooled into a common list by procedure and any consultant may do the operation.
This ensures the longest waiting patients are done first regardless of whose care they are under.
[NB. When you have had the operation, write down the name of the doctor that actually did it, and place that in your medical record.]