How long is a piece of string? There have been cases of days, weeks, months, years, and never. Generally a few weeks to a couple of months.
If you want the best information use your phone number in this BT Wholesale checker
. Watch there for availability for your line to go live, rather than relying on contact from your registration.
If you don't have a number acceptable to that checker, use this address checker
. Don't use the postcode checker.