I think most villages had somewhere for paupers to be housed, prior to 1836, but it may not have been a formal "workhouse". And there's not usually any records.
Some parishes have Vestry records, which may contain references to whatever was classed as a "workhouse" or "the House", but a look at the Northants Record Office catalogue isn't showing me any for Harringworth.
Once the big district workhouses arrived in about 1836, everything got a lot more formal, and the local Guardians of the Poor who ran the Workhouse had to ensure that the expenses for paupers in their care were allocated to the correct parish - no-one wanted to pay for another parish's paupers! The more paupers there were, the higher the Poor Rate everyone had to pay.
That may explain why there were suddenly removal orders - returning paupers to their place of settlement. Or it may be just that the record keeping was better, or more records have survived.