So, as far as we know, there have been no sightings of the couple since they appeared at East Ham station in NE London by mid-day on Saturday 7th January. That´s now a full week ago.
Considering how jam-packed London is with CCTV cameras, it seems quite amazing if no cameras have been recording the pair for a week...Which makes me think that they´re likely staying in the local area of Newham/East Ham. This is also very close to the location of the then main campus of the actor´s school where Constance Marten was a student around 2016. She likely knows the area very well since that time.
They are likely not that noticeable, especially apart and or without the baby. Alone she's a nondescript white woman doing some shopping.
I wouldn't be surprised if she doesn't quite look like the photos put out there either. A priority for missing persons investigations is to get the most recent clear photos of the people missing as possible for media releases. Whether the photos used are from arrests or driving licences (and honestly they could be either) they are unlikely to be all that recent. They're also not great for recognising someone. Super close and washed out, flat harsh lighting, his has a weird focal point which I'm sure is warping things a bit too. Not what you'd pick if you had options. Especially as, even if she/they were arrested recently, police don't use a mugshot for a press release unless they really have to for obvious reasons.
Now it might be that they initially used them because they'd come from out of area so the police force who realised they were missing from the car with a baby, felt the risk was high/immediate and only had these photos to hand (in which case they're mugshots) - but no new photos have popped up or been released either. No cropped group shot, no pic of them standing together, no family pictures with the other kids, no smiling selfie. The only other photos of her attached to articles is from at least feb 2020.
So it seems despite all this manpower they haven't got hold of a better photo of them, not through family or friends even. That's... Well it's odd on it's own, but my main point was that if it's been a rough few years for her, she might pass under the radar fairly well.
The problem for them is when they want to move as a group. Older rougher black dude, white woman with a posh accent and a days old newborn - but no pram/nappy bag/baby stuff etc. Even in London they run much more of a risk of getting noticed and recognised.
A house search is also usually a top priority, but I've not seen much coverage about where they were living before all this started.