Sky perform a check with a credit reference agency (Equifax), but it is not a conventional credit check. If you request your Equifax file - costs £2 and you can do it online - you'll see that where you've actually applied for credit from real credit companies, the enquiry is logged as a "Credit Application". The search performed by Sky is logged as a "Preliminary Enquiry" - a different thing, however defaults will be recorded.
Sorry not sure who BT uses for sure, I gather that BT private uses one credit agency while the business side of BT use another agency, but not sure which uses who in this case.?