Dear Alexander,
You are correct in using the expressions, ''It's high time I did some work.'' / ''It's about time I did some work.'' / ''I had better do some work.'' All of these versions share the same meaning of immediacy.
In the past, you might say something like this: ''I felt the time was right to do some work.'' or, ''It was high time I did something about the matter.'' for example..
When using Reported Speech, one might say, ''The teacher told me (that) it was high time I did something.''
Hope this helps you in your query!
Max