The line chart illustrates the percentage of UKthe UK's population whoich watched radio and television programmes during 24 hours of a particular day in 1992.

Population = who, but percentage = which (or that)

Overall, the radio audience reached its peak in the morning and steadily dropped throughout the whole day, whereas the audience of television programmes increased gradually during the afternoon and jumped closer to the evening hours.

Throughout sort of implies whole, but I just thought this sounded better.

Both the television and radio audiences stayed at their lowest amount during the night.

Again, amount is sort of implied, but this sounds better either way.

The morning showdata revealed people were mostly listening to the radio thaninstead of watching television.

rather than also works here.

I suggest the word reveal instead of show because it fits the academic register well. If the correlation is less direct or obvious, you could use the word suggest.

The hours between 8 and 10 o’clock were the highest peak ofFrom 8 to 10 o’clock were peak hours for the radio audience, with roughly 30 percent of the population tuning in, whereas the television audience was made up by less than 10 percent of the population.

This was a complicated idea to express, so it's harder to phrase as elegantly as your other ideas. I just rewrote it in a way that sounded natural to me.

While the radio audience fell steadily, the relative amount of the television audience started to grow since thefrom lunch time and increased sharply by (at?) 6 o’clock, leveling off at approximately 45 percent of the population from 6 toby 10 o’clock.

A sharp increase would not happen by (before) a certain time, but at or around a certain time. But the leveling off could just be shortened to 'by 10:00' because 6 is already implied.

The line chart illustrates the percentage of the UK population who listened to/watched radio and television programmes during 24 hours of a particular day in 1992.

I added "listened to" because you can't watch the radio

Overall, the radio audience reached its peak in the morning and steadily dropped throughout the whole day, whereas the audience of television programmes increased gradually during the afternoon and jumped closhigher toin the evening hours.

The morning statistics showed that people mostly listeninged to the radio rather than watching television.

sounds better like this

The hours between 8 and 10 o’clock werehad the highest peak of the radio audiencelisteners with roughly 30 percent of population, whereas the television audience was less than 10 percent.

While the radio audience fell steadily, the relative amount of television audience started to grow since the lunch time and increased sharply byat 6 o’clock, leveling off atwith approximately 45 percent of population tuning in from 6 to 10 o’clock.

I changed it to "increased sharply at 6 o'clock" because I think you mean at 6 o'clock, the number increased really quickly compared to earlier.

"tuning in" is another word for "watching"