I think robbery as a motive (with Parry or anyone else as the thief) can safely be ruled out. We only have Wallace's word for the insurance money being in a tin in the kitchen and that it was missing. And according to him it was only four quid! I know four pounds was worth more then than it is now, but even so it was hardly a fortune worth murder and being hanged if caught. Also, Mrs. Wallace's purse with money and silver was lying in plain view on the kitchen table and wasn't taken- neither was her wedding ring. If Parry did it then robbery wasn't the motive and he was acting as Wallace's hired killer. That is a possible theory in my opinion, but too complicated in the end. I think the simplest explanation is that Wallace himself murdered his wife and created red herrings to draw attention away from himself. With robbery removed as a motive, the only person who would want Mrs. Wallace dead and have the means and opportunity is Mr. Wallace.
if Wallace had wanted his wife dead then he wouldn't have had to go to all that palaver of setting up a false alibi and beating her brains in then wandering the streets looking for a place, and a person, he knew didn't exist.
He could have opted for the more genteel way of simply pushing her downstairs or poisoning her (he had a laboratory in his house remember?)
Julia was frail anyway and it wouldn't have taken much to do away with her.
When Wallace was 14 years old, his family moved to Walney Island, Barrow in Furness- which is across the bay from the Isle of Man. It's the perfect region of the country to encounter the rare surname Qualtrough. Could this unusual name have stuck in Wallace's memory to be fished up conveniently many years later to provide the name of the mysterious telephone caller? Wouldn't it have been better to use a more common, and therefore more untraceable alias such as Smith, Jones or Brown? Maybe Qualtrough was his own little private joke.
Louisa- Husbands who kill their wives go to a lot of trouble setting up alibis and false alibis. As for poisoning- it takes time to achieve and attracts attention, and it can be messy. Besides, it's a huge step from tinkering with chemistry sets to having knowledge of, acquiring and administering poison. Pushing his wife down the stairs could look like an accident but it wouldn't necessarily be guaranteed to kill her- and what then? The stairs in those kind of dwellings are hardly precipitous. Bashing her brains in quickly, distancing yourself with an alibi and casting suspicion on a strange intruder is a better bet.
Hatchett- Good point about Qualtrough being memorable. It certainly is that! In the same way he called attention to himself on the night in question while on his futile journey to find the non-existant Melove Gardens East. THAT name is memorable as well. And having Parry- or anyone else- in the frame would have suited him. All little arrows pointing away from him- pointing anywhere than at him. But common sense dictates to me that no one else but him is the perpetrator.
And yet there's almost no way he CAN be the murderer. He was a frail older man, recovering from a significant illness. Between the last solid sighting of Mrs. Wallace and his boarding the trolley there was barely enough time for a much younger and fitter policeman to make the distance with a scant 10 minutes to do the (rather messy) murder, get cleaned up, and leave. He was not in physical distress or even noticeably winded by his apparent sprint even though the police officers (multiple tries) were.
There was no trace of blood in any of the drains, nor was there any bloody clothing found in or around the house. Beating someone to death is a messy business- whoever did it got blood on them, guaranteed. There was no sign of blood on Wallace.
Although he is sometimes presented as being a chess master, from what I have been able to find, he was an enthusiastic amateur but by no means the ace of his chess club.
He was, as far as can be determined, a dull little man in a dull little job leading a dull little life. If by some quirk of fate he decided to kill his wife (who he never showed any signs of intense dislike for), would he kill her in a dull little way or suddenly have a singular flash of criminal mastermind inspiration and create a murder mystery we are talking about 80 years later?
The same issues do not apply with Lizzie. There's neither a physical reason she couldn't have done it (healthy woman) nor a time issue (she was admittedly in/around the house and didn't have to get from anywhere to anywhere).
With Wallace, there are many problems with him being the murderer- logistics indicate that he couldn't have physically done it. We will never know if he had motivation to kill his wife, but he did not have the physical ability to do it in the time-frame as we understand it.