You can search the GP Register (for primary care clinicians) and the Specialist Register (for hospital doctors). The Register will not tell you where a clinician is currently working. But as others have said, many hospitals have lists of consultants and their clinical teams on their websites, listed either by department or alphabetically.
Consultants will often be working for both the NHS and for local private hospitals, so you may also find a consultant plus his or her biography and areas of clinical interest listed on a local Nuffield or Circle Health Group website.
Our GP practice will send copies of test results via email if the patient does not have access to the surgery's online patient record portal or to the NHS app.
But communication with hospital consultants and clinical departments is usually via paper letter or by telephone. I have had the findings of an ultrasound scan discussed on the phone by the consultant who had ordered the scan as soon as he had received the report when the radiologist had reported a strong suspicion of malignancy and to tell me that I was being referred to oncology for further investigations under the 2WW pathway. But usually I am given results of scans or biopsies at face to face appointments or via paper letters.
All hospital consultants have NHS secretaries who may work for two or three consultants. They will communicate via telephone and email. Their names and email addresses are often included on the follow-up letters dictated by the consultant for whom they work.
Secretaries may use an NHS email address ending in nhs.net but each hospital has its own email address, for example, the secretaries at my local hospital have email addresses ending in this format and this is the format mostly used by them when responding to patient enquiries - not the nhs.net ending:
uhd.nhs.uk
It is not unusual for paper letters typed up from consultants' dictation to contain typos - so I would not be too suspicious if these alleged communications contain the odd typo.
But I would be looking closely at the message source details in these alleged emails that the sender's name and email address matches the secretary's details, as consultants don't as a rule communicate directly with patients via email.
If there is a secretary's name and email address, you may also be able to find these on Google searches and sometimes on the hospital's website along with the consultant's bio.
Appointments for scans and tests are usually sent to the patient by paper letter, though we have occasionally had phone calls offering very short notice tests with no confirmation of the appointment date by letter sent out, as there would not have been time to send these out before the appointment.