Maybe he was already in East Croydon at the time, and therefore didn't have to make any effort to meet her. He said she travelled on her own a lot and was responsible, so it's completely illogical that he'd have made a special trip to pick her up - for what? I think he must have already been there for some other reason.
BBM
Is it possible they met by by prearranged plan so SH could give TS the ten pounds (promised her by CS, perhaps) in order she could buy the 'flip flops with straps' she was so intent upon having ?
Is it possible SH had just drunk the ten pounds, prior to meeting TS? If so, did he make excuses for not giving her the ten pounds then and there? Was she sulky? Did SH tell TS he'd left the money at CS's place? Is it possible this is the reason TS didn't just buy her flip-flops and go home to NS's place (remembering the various stories we've heard, some of them being DN claiming TS was due at NS's place by 6 ) ?
Did TS accompany SH reluctantly back to CS's place simply to get her ten pounds?
Did SH attempt to mollify TS with chips, pizza, computer games, more excuses?
Did TS insist on having her ten pounds regardless?
Did SH claim CS would give it to her when she came home?
Did TS decide there was no point going home if she'd have to return to CS's place next day to collect the ten pounds?
Did SH start to panic at the thought of CS arriving home only to discover an angry child awaiting ten pounds that SH had already blown on liquor? Had he done the same before and been told next time was his kick out the door?
Did he finally deliver a sharp slap to the side of TS's head, knocking her half unconscious? Did SH really panic then about what would happen when she came-to? So did he hold something over her face and finish it, afterwards stuffing TS in the loft?
Did his story start to fall apart in following days, with family members questioning him in greater depth? Did he finally confess in response to their accusations?
Was it decided to cover it up, for fear NS would lose custody of her other children and SH would go to prison in tandem with in-depth investigation into the entire family?