It depends what, or when(?), you define as the Middle Ages. I can answer for the later medieval period.

The population of London was around 50,000 in the year 1300, this figure is arrived at through documents relating to taxpayers and similar sources. However, it is often ambiguous if this figure includes the city of Westminster and Southwark, or just the city of London proper.

The data indicates that there had been steady growth in London following the Norman invasion when London’s population was around 10,000. Throughout the period London saw influxes from other areas of England and from Europe. For example, there was a notable Flemish community of a couple of thousand living in Southwark and Italian merchants were also known to be in the hundreds.

As for the low point, we can say London was smallest before the growth introduced following the Norman invasion. However, it is more interesting to examine the effects of the Black Death on London’s population, with estimates suggesting that 50% of the population was lost. Even more notably, the population did not immediately return to the earlier numbers despite London remaining a convenient and profitable location. It took at least a century for London to return its pre-Black Death figure, and since then the growth has been exponential.

So in answer to your questions, it depends what you mean by London and it depends what you mean by Middle Ages. But the short answer is 50,000-ish for the highest point and 10,000-ish for the lowest point. But with lots of interesting dips and rises along the way.

Sources:

The best work on later medieval London in my opinion is Caroline Barron’s London in the Later Middle Ages: Government and People 1200-1500