Using birth date and birth registration data from my one-place study, I was able to assess how many births occurred in the year they were registered. The data is from all the individuals on the 1939 Register in an East Midland parish, born more than 100 years ago (1916 or earlier). The corresponding GRO birth index entry was located for each 1939 Register entry. I was able to match birth dates with birth index entries for 211 individuals in the parish in 1939.
First, I looked at how many births were registered in the quarter in which they occurred. For example, how many of the January births were registered in March quarter. This is easiest displayed graphically. From this we see the expect trend – births that occurred at the beginning of the quarter were registered in that quarter, while births that occurred near the end of the quarter tended to be registered in the following quarter. From this we can see that, for example, 100% of April births were registered in June quarter, while only 13% of June births were registered in that quarter:

More interesting to look at is the subset that were born in a different year to the registration. Unsurprisingly, these births were those registered in March quarter that correspond to births in Oct-Dec of the previous year. Interestingly, 100% of December births in this dataset were registered the following year, while 33% of November births were also not registered until the following year:

Finally, looking simply at the percentage of births registered per quarter that actually occurred in that quarter:
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Quarter | Born in quarter | Born before quarter
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Mar | 72% | 28%
Jun | 58% | 42%
Sep | 53% | 47%
Dec | 60% | 40%
From this we can see that 28% of March quarter births actually occurred the previous year. From this data, I would conclude that it is reasonable to assume that the birth registration year is the same as the birth year only if the birth was registered in either June, September or December quarters. However, there will no doubt be a small number of exceptions where even this assumption fails. For March quarter births there is high likelihood that the birth did not occur that year, and should not be entered into our family trees without some indication that the year is an approximation.