From Clapham Junction you can get the Overground which goes to Wembley Central via Willesdon Junction (may have to change at Willesdon) which may be the best bet. Overground every 15 minutes. I may well do that myself if theres no tube as my train north goes through Clapham J.
Looks like we would have to change at Willesden Junction to pick up the Bakerloo line, which may be affected by any strike.....but it is an alternative and there must be buses from Willesden to Wembley, or we just join in the walk.....