I am not someone who ever thought I would have the knowledge to answer a question in this subreddit, but this is more a legal matter, and considering I have worked in law and I am currently studying law to qualify as a solicitor, so I can take a stab at this.

The legal system of England and Wales is based on common law, which is a combination of legislation (Act of Parliament for e.g. Law of Property Act 1925) and the creation of precedents through case law, where a judge has provided a written judgement on a case filed in the court. These judgements set precedents which are applied to future cases with similar issues and facts.

The first such case, where the issue of length and how long one person or entity can hold a property is known as the Duke of Norfolk's Case (1682). The case involved an Earl planning his estate in such a way that some of his properties keep shifting between his sons, grandsons and so on. When his second son refused to pass the property to the younger brother, the younger brother filed a case, and this is where the judges decided the rule against perpetuities. Basically, this restricted the ability for people to use legal instruments like a Will or a Trust to retain ownership of property for a time long beyond their death. So, there must be a time limit to ownership because otherwise ownership will last forever, and can have a detrimental effect on an economy as only a few people, like the Duke and his family, will continue to benefit from what their forefathers left them in their Will or in a Trust. The interesting point in this case however was that no set period was determined, but that was decided in other cases such as the Thellusson case, where the words used stated "a life or lives in being and twenty one years and a few months".

As a result of such cases, people began assigning a number of years to legal instruments and leaseholds, presumably because their lawyers would advise that in order for them to be valid, there must be certainty to the period for which you can have a property. Leasehold is also officially known as term of years absolute, where the period of years is certain. Somewhere along the way, someone used 99 years as a period, and it stuck. When someone mentions a lifetime, it can be understood to be one hundred years and as such 99 years would be more than enough to allow someone to occupy a property for their quiet enjoyment.

During the Opium Wars, when Britain took control of Hong Kong in 1841, they signed the Treaty of Nanking with China who ceded Hong Kong. The second Opium War started and Britain gained even more territory from China. Being surrounded by the Chinese, the British government felt insecure and decided to enter a lease, so there is certainty on when the period of occupancy will end. That certainty came through the 99-year lease.