I suggest that you see your GP to get their help in trying to get a clearer picture of what the neurologist is saying. No evidence on the lumbar puncture presumably means you don’t have oligoclonal bands in your cerebrospinal fluid. And 5% of people with MS are negative for O bands, which is perhaps why he hasn’t made a definitive diagnosis. Also no changes to MRI, I imagine that means you’ve had more than one?
To get an MS diagnosis, the neuro is likely to be following the McDonald Criteria: https://www.mstrust.org.uk/a-z/mcdonald-criteria This means that fairly strict criteria are followed, which you can see on the MS Trust webpage. Generally it’s having two or more lesions on MRI separated by time and space or at least two relapses and at least one lesion. While for progressive MS, it’s a positive LP plus progression over a period of 12 months in addition to MRI data.
So I suspect that while you have a negative LP, the neurologist perhaps doesn’t have the clinical data to support a diagnosis. But is fairly confident that you do in fact have MS based on your history plus neurological exam and MRI data.
I’m sorry if this all appears a bit negative, but judging from what you have said, there’s little more to suggest apart from talking to your GP. At some point your neurologist will send a letter to your GP detailing his findings and recommendations and you will receive a copy of that letter in the post. One thing you could perhaps do is phone the neuros secretary and ask if the letter has been written yet. In my experience, weeks or even months can go by before the letter is produced, sometimes it will state the date the letter was dictated (often very soon after the appointment) and the date it was typed (weeks later). So it might be that you hurry up the typing of the letter by phoning and talking sweetly to the secretary!