I know quite a lot about the photos, but nothing that is really relevant to identifying the bike. Bear in mind that I know very little about bikes from the pre war era in my next comments.
There are four things that do strike me as being unusual about it though.
First, the handlebar levers. They appear to be of the later type that is common even today. My original guess as to the bikes age was based on these, so I would have dated it as being closer to WW2 than the registration date.
Second, the headlamp appears to be chrome. From other photos, it seems that this is unusual, most being black. As suggested, it could have been changed at some time.
Third, I cannot ever recall a rigid framed bike as not having a rear mudguard strut that comes roughly 45 degrees away from the hub. No doubt there are some, and if there are, I'm certain someone on here will know. Perhaps that will help to identify it.
Fourth. the exhausts seem a little short. When I have trying to identify the bike, similar systems are always longer.
Years ago, I was told that the bike was a 328cc OEC Twin Port. I've since discounted that one. Then, I was told that it was a 1938 Sunbeam Model 9. That does not seem to be correct either, especially if the registration is from 1934 or 5.
One thing that may be relevant. In June, 1951, the owner of the bike wanted to take the little lad in one of the photos (his nephew) to Chester Zoo. That would suggest to me that it was a 5 or 600cc engine. Mainly because to take a child of that age with him would suggest it had a sidecar. I couldnt really see anything smaller being used as an outfit.