Detectives went to Shorrolds Rd within minutes of her disappearance being reported at 6.45 pm, acting under an order to "enter and search" (Andrew Stephen page 10). A police guard was put on the door.I agree with you when you say it would have been critical in the timeline as to when MG first went to Shorrolds Road. However, MG would have told them that he didn't have a key to the property, so why did the police not visit Shorrolds Road that evening? Instead, they broke into Suzy's flat.
MG would also have told them about her diary entry for 37SR that day, and that she hadn't been seen since the so-called viewing that lunchtime. I don't understand why they left it to the following morning to visit the property, It should have been their first port of call.