Mechanized textile manufacturing was famously one of the early components of the industrial revolution, and cheap mass-manufactured textiles were perhaps the single most economically significant component of Britain's industrialization in the 18th century. This depended on many mechanical advances by a variety of inventors. Did it also depend on progress in agriculture, and specifically cheap cotton?
By analogy, the development of the printing press required the development of cheap paper. Before paper made its way to Europe, most of the cost of printed material was in producing vellum to write on, and mechanizing the printing process would have been economically unfeasible. It was only after the inputs became cheap that there was an economic niche for Gutenberg and his predecessors to develop. It seems possible that textile production was in a similar situation.
On the other hand, while British agriculture had improved dramatically in the period before Arkwright and others mechanized textile production, AFAIK the British textile industry depended on cotton imported from Egypt, India, and later the American south, and cotton was not grown in Britain itself. So it's not clear to me whether cotton became cheaper in the period before textile mills, and I don't have a good sense of what fraction of textile costs was in agriculture vs refining and production.