Hi,
If you intend visiting this year, most record offices allow you to photograph documents the cost is about £6 per day for this.
Possibly an easy way to see what each record office hold is to do the following using the link below:-
https://discovery.nationalarchives.gov.uk/Enter only the Surname - Farrell in the search box
Do not enter any dates
Click on box "Held By" and from drop down list select "other archives only"
You are now presented with a list of results. On the left hand side you can select date but more importantly which record office hold records in which Farnell is mentioned.
Suggest you select date 1700 - 1799, and Leicester. Click Refine.
You now have all documents held by Leicestershire, making a list of which you wish to examine
you can then make an appointment at this record office and pre-order the documents. This can then be repeated for Derbyshire etc.
Do you have access to either Ancestry or Findmypast?
Spendlove