The activation signal does not after all seem to have been sent out by India so I called 01506 677000 at 10.58pm only to find that it was closed, supposedly at 11pm according to the recorded announcement that was played to me.
However knowing customer services at Sky is open 24 hours a day I looked up the other numbers listed on saynoto0870.com for BSkyB and found 020 7979 9500 in the Unverified list. I called this and it led to a full IVR menu system that included various options including 3 for everything else and then another menu number for billing and accounts at the next menu.
After holding for 10 minutes or so I was connected to a very helpful lady with an Irish accent in a UK call centre who was able to look up my details and have the activation signal sent again.
So if you need to speak to Sky between 11pm and 8.30am then make sure to call
020 7979 9500
and not 01506 677000 as 01506 677000 merely plays a message saying they are closed at that time of day.
EDIT:- 020 7979 9500 also works during normal office hours Monday to Friday with precisely the same menu system. However as I suppose it may take up internal voip bandwidth at Sky redirecting the calls to Scotland it is probably best to stick to the normal 01506 number between 8.30am and 11pm. This number is listed at
http://whocallsme.com/Phone-Number.aspx/02079799500 as being an outgoing CLI number for calls by Sky Broadband.