This is my scenario synopsis as the way I think it could possibly have gone on the night/morning of that fateful Thursday/Friday 2 weeks ago. Lot of 'possibles' as we don't know certain facts as not revealed, so bear with me.
I am basing this on LS living on Wellesley in one of the even numbered houses, and not an odd number, ie one that backs on to the Drain. I am still not sure if that has been confirmed by any means, the number? Have seen several options mentioned here. If it is this house, 32, below, then my theory might hold a little more water! If not, then I am not even close.
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So, on that night the occupants are out to a party first before going on to the Welly. We know LS didn't seem to take a bag with her so she may either have not taken a key as she was travelling light (no phone either), or that as the occupants were all out together, and intending to return home together, she didn't really need one as one of the others was the 'designated house key holder' that night, perhaps having taken a bag with her.
As events transpired, LS left the club before the others and the key was forgotten about. Somewhere on the journey in the taxi she realised this fact. So when she arrives at Wellesley, knowing she can't get in, she doesn't bother going to door as she knows no one is home, instead heads down Wellesley, turns into Beresford and walks on down to Beverly intending to get a bus back to the Welly.
As she crosses over Beverly to the stop, she is caught in the headlights of Mr Grey Hair's car as he approaches, and notices the obviously worst for wear young woman. Someone said on here that she fell on the ground although we have no proof of that, but that might have alerted her to his attention: she falls, it's icy, it is below freezing and she has no gloves and is wearing no tights. If she did fall, she would have hurt and possibly grazed or cut her leg and hands, so she may have started crying as witnessed being 'distressed'. Or, she may have got to stop, and found either the last bus had gone, or that she had no money as had used last she had on the taxi, and because she didn't have her phone either, she couldn't use contactless payment. So she starts crying as cold and drunk and doesn't know what to do - then seen by Mr Grey Hair.
At some point after that, either she decides to head back to Wellesley or she is spotted either by PR or whomever is the man on the Haworth Street CCTV.
The first scenario. She staggers back across Beverly Road and back down Beresford where at some point she is seen by a predator on the loose who follows her.
As she gets to the junction where Beresford meets Heathcote, she turns left, and then veers right into the pedestrian only pathway that cuts through to Wellesley. Remember the woman in the house on Heathcote who heard the screams (I shall return to her shortly) said the street was used as a cut through:
"We do get a lot of students who live in the road that Libby lives in who use this road as a cut through."
I think she may have meant this pathway, particulaly if she lives in one of the houses closest to it.
Halfway on the left of this pathway there is a short alley that backs onto the end row of houses on Wellesley as mentioned above. If LS lives at 32, you will see from pic in the link there is a gate to this alley from the garden (possibly same with adjacent houses?)
Back to the Heathcote woman. If she lives in one of the houses that also backs on to the alley from the other side, I wonder if her bedroom is at the back of the house? It is more usual for bedrooms to be at the back, although admittedly with some that are in multi-occupancy I appreciate they can sometimes be at front. But let's for argument sake say her bedroom was at back of house, I wonder if the screams and noises she heard were in fact emanating from this alley and not from Heathcote Street itself?
Back to LS who has turned onto this alley from the pathway. She has remembered that they sometimes use the back gate entrance as it is not locked (just hypothesising here) and she thinks she'll get in that way. As she is here, she is caught by the one who has followed her. So what the woman in Heathcote heard is her scream, the voices and the bang of the garden gate as she is perhaps pulled sharply back from it whilst she has hold of by the attacker. Alternate scene, she is not followed but someone is already lurking here who she encounters and same scenario. This could be random or someone who lives in one of adjoining houses - and gate slam may be pulling her inside their own (I don't know if police have searched all gardens and houses in that section?)
In the second scenario, PR or car guy sees her on bench and asks does she want a cab, he is a mini cab. She may be crying and says she doesn't have any money, he says never mind, he will take her, his car is just around corner, come with him. She does that.
If PR, if what sister says is correct and he is well meaning on this occasion, he drives her back to Wellesley, good deed done, and she gets out and off he goes. LS turns into the same pathway to cut around to the back garden gate, but approaches from the Wellesley end - and same fate befalls her as above.
If PR as not Mr Nice Guy, he drives her back to Wellesley, she gets out. He looks around, road is clear no one around, house lights along street all off, he spots his chance, gets out of car and follows her down the path, to alley and attacks her there. He could then drag her the short distance to his waiting car.
I am afraid I draw a blank as to what happens after that. If not PR or someone who drove her there, then I think she could be in one of the sheds or houses that back on to alley. If taken by someone with car, then...who knows.