It was Mr Harding that my secretary sent the bill to yesterday.
It was Mr Harding who my secretary sent the bill to yesterday.
Is" who" possible in stead of "that" when a personal object is emphasised?
These are cleft sentences.
Both the sentence are grammatical. You can use the relative pronoun that or who in the sentence. The use of the who is more common. Besides, you can drop the that/who in the sentence:
It's Mr Harding my secretary sent the bill to yesterday.
Reference McMillan Dictionary: It's your brother I want to talk to.
For a singular person, you can use either of them. But, it's preferable to use "who". For example:
Peter, who was a fine marksman, shot the thief with expert accuracy.
However, you can use “that” when referring to someone you don’t know personally or have a name for. For example:
The guy that came to fix my water pipes last year said the pipes were very worn.
In fact, going by the rule of he/him, I'd suggest you to use "whom". So in your case the correct sentence would be,
It was Mr. Harding whom my secretary sent the bill to yesterday.