Project was put on hold back in March due to lack of funding and the TFL finance crisis . Even if it did get resurrected , it could take another 5-10yrs before construction even started and then another 5-7yrs of construction . So best case you can sleep easy for another 15 yrs+.
The safeguarded route was under Wandsworth common flowing under Bolingbroke pub and across hiller , montholme and gayville roads . But that safeguard was dropped as part the project suspension and the argument of whether Balham or tooting .