We checked the same search for a surgeon from 25 spots around your practice around Headington in Oxford. Overall, your practice is far down the list in most places, and the map does not show it first or in the top three anywhere, so it looks weak almost everywhere. Each dot is one of those spots; Green means the practice is in the top three there.
This may mean that, from the weaker parts of the area, someone searching nearby may not come across your practice.

Oxford Hernia Clinic appears both closer to the address and further out around Headington in Oxford, while your practice is far down the list, so this is the gap worth understanding.
This is the same search from the same spots around your practice, so you can read the two maps side by side.
This suggests a wider local presence is reachable around Headington in Oxford, and the first thing worth checking is whether both practices offer the same services.

This estimate did not find searches using your practice name, so people reaching your site through Google are not yet searching for you by name.
Next, we will look at which searches can bring people here without the name.

These are non-name searches about hepatobiliary surgery and Churchill Hospital information, but the ones found sit beyond the first page, so people who do not know you are unlikely to reach your site this way.
The key point is that, around Headington in Oxford, someone looking for hepatobiliary surgery is not reaching you this way yet. That gap in finding your own field is the main finding.

There is real ground already in your favour here, and a few gaps worth attention. Both sit on the same page, and all of it is workable.
I used to run clinics myself, so a call is just two colleagues looking at the same page. None of this needs solving at once; each piece can be taken on its own.
Patients choose before they call: from the first names on the map, from the first results on Google. My team rebuilds what decides that, your Google listing and the pages a patient lands on, and keeps it up every month. Here is what happens if you reply.
WhatsApp or a voice note. Tell me which part of this page matters most to you. I reply myself.
We agree the priorities and what Forge will deliver, in writing. It is the only real time this asks of you.
Your Google listing and the pages a new patient lands on. Fixed before anything is built on top.
Kept up month after month. You watch it in a shared table, with a regular call, and your own people kept in the loop.
Four practices, four kinds of work. Delivered, not promised.
See the projectsEvery page about implants rebuilt, down to the questions patients ask before deciding. Kept up month after month.
The page patients land on before they book, her Google advertising, and a weekly letter to the colleagues who refer to her.
Every question his patients ask, mapped, then written and linked from his own publications.
His whole site reviewed page by page, and the three-month plan, city by city.
For a given specialty. So we do not work with the practice on the second map above, and would not while working with you.
Then very little: the odd decision, and your clinical eye where it matters.
If you stop, you keep all of it. No minimum term.
Agreed in writing. Nobody honest can promise you a position on Google, and we will not.
I'm a doctor. I used to run a group of clinics, and I know this part of the job is not why anyone chooses medicine. Today my team does it for practices like yours: the research, the writing and the set-up. You come in only where clinical knowledge matters.

WhatsApp or voice note: +33 7 43 69 81 74. Tell me which part of this page you want to understand better. I reply myself. This page was made for your practice only, and it comes down 32 days after it was published.
The questions practitioners actually ask me after a page like this.