You asked about apprenticeship records in the 1800s. From 1710 to 1804 there was a tax on apprenticehips so reasonable records have survived.
After 1804 (actually 1811, allowing for stragglers) there was no tax and no need for any official record. Basically, you'll be very lucky to find anything because apprenticeships would then be purely private agreements. For pauper ancestors, the best chance of finding details of an apprenticeship would be among the poor law records.