They did not give themselves time to do so, though, and then they were committed to their narrative.
Getting into Shorrolds, finding the car, searching Stevenage, and talking to AL kept them busy till 0330 next morning. By mid morning they've got HR with the artist and they've decided to go for the 2pm press conference at which that sketch was brandished.
They arrested 30+ people that day for the cement factory fraud, so they simply did not have time to take statements and cross compare them while simultaneously preparing for the press conference at which they told the TV cameras that SJL went to 37SR and was seen there.
If they'd held that conference 2 days later I'd be less sceptical, but they did what they did and then pronounced the results of the appeal for further sightings 'disappointing'. Well, it would be if you're appealing for sightings of something that didn't happen. Given HR's demonstrable flakiness and tendency to tell you what you wanted to hear, this should and possibly was enough to suggest that Mr Kipper was MG, but how popular would you be if, a few days after that press event, you said Er actually there may never have been any visit or any Mr Kipper? MB still maintains that all we know is SJL left the office at about 1240 and her car was seen at 10pm. It doesn't sound like he buys Mr Kipper either.
I don't think it's safe to eliminate possibilities on the basis of what the police would normally have done, if the timing suggests they left themselves no time to do so.
There is a issue with the way you consistently misquote the circumstances and place unwarranted negative bias on what has been reported.
Report the facts as they are, like them or not, instead of rebutting them without any supporting evidence.
The escalation of such a missing person enquiry into a major investigation is a well established and effective process.
1. There were more than enough CID and uniform officers to deal with the initial missing person report (uniform/DI Johnstone), house searches (37 SR and SJL's flat - CID), statements from HR and MG (CID), street search (uniform) and securing the vehicle until the following morning (uniform), elimination interview of AL (CID - early AM 29th July)
2. DI Johnstone and DS Barley were involved in the cement factory early morning raid on Wednesday 30th, the day AFTER the press conference. They were back in the office a few hours later. D/Supt Carter was still SIO, during this time. AMIP detectives don't need their hands holding......they are exceptionally experienced. (AS (p.36-7)
3. D/Supt Carter was the next SIO on the rota from AMIP (Area Major Investigation Pool). He was in the office at 06:00 the following morning. Due to the circumstances he escalated the enquiry, internally, to a murder investigation. Time was of the essence to find SJL's body to provide the best opportunity to solve the crime. Hence the need for a press conference without delay. The police needed witness and information asap to identify additional lines of enquiry, not wait for two days twiddling their thumbs. (AS p.20, 22, 29-31)
4. HR gave a first description to MG, when he went looking for SJL. There is no reason for this not to be an accurate and reliable account of what he saw (AS p.8)
5. We know that HR spoke to MG directly. HR did not describe MG to MG, that is absurd! (AS p.8)
6. MG is just repeating what DS Barley said about the undisputed facts, that SJL left the officer at approx 12:30 and that her car was found in Stevenage Road at 22:01. That is just fact being quoted....nothing more, nothing less.
7. Do you have the experience of major investigation to make a judgement on what can or can't be achieved in a certain time period?
8. Uniform officers and the Duty Inspector will have picked up the initial missing person report and liaised with the on-call CID, who contacted DI Johnstone. DI Johnstone provided the initial investigation supervision and tasked the duty CID and uniformed officers via the Duty Inspector (Uniform). What was required was perfectly manageable with the significant resources as the time.
9. Once D/Supt from AMIP had been tasked he came with a team of specialist detectives manage the investigation, in addition to DI Johnstone, DS Barley and other local CID officers.