You only have to look at the population growth. We have had two periods of significant population growth since the war2, a period up until the 1970, the baby boomer period combined with some limited immigration. After this period our population was relatively stable for about 20years. Then we have had a significant popukation increase since the mid 1990s. I assume you are not disputing this later increase in uk population ? If you do not, what do you put this population rise down to? It can be only one of two things? either a sudden increase in uk residents deciding to have more babies or immigration?
Apart from net migration, there are two main drivers in the increase in population - more births and less deaths. Life expectancy increased around 6 years between 1990 and 2020.
1999 was the first year in the 90s, where net migration outstripped changes in the existing population. And you're right, there was a baby boom a few years after that. You can see it on the chart below, just how much births fluctuate (and of course the pattern can repeat, as those 'baby booms' will also produce their own baby booms).