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Final Answer:
Mrs. Middleton, the housekeeper.

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Explanation:
Let’s think step by step:

1. Mr. Pace was murdered in his house the previous night.
2. His nephew, Mr. Havering, was in London visiting Hercule Poirot at the time — so he has an alibi.
3. Mrs. Havering is Mr. Havering’s wife. If her husband was in London, and she was with him (as implied), she likely also has an alibi — though not explicitly stated, we assume she was with him unless told otherwise.
4. Mrs. Middleton, the housekeeper, *mysteriously disappeared the next day* — right after the murder. That’s very suspicious. People don’t usually vanish unless they’re hiding something.
5. Mr. Smith (shopkeeper), Mr. Fitzpatrick (butler), and his wife, and Mrs. Waterbrook (friend) — no info says they were missing or had opportunity.
6. The detectives (Poirot, Hastings, Japp) are investigating — they’re not suspects.

The key clue is: Mrs. Middleton disappeared the day after the murder. That strongly suggests she did it and ran away to avoid being caught.

So the murderer is Mrs. Middleton.