Hi Rosie,
Yes you are correct! Richard was the son of James Ellwood. I have found a document on Ancestry:
'''Legal Record''': "UK, Articles of Clerkship, 1756-1874"<br/>The National Archives of the UK (TNA); Kew, Surrey, England; Court of King's Bench: Plea Side: Affidavits of Due Execution of Articles of Clerkship, Series I; Class: KB 105; Piece: 6<br/>{{Ancestry Sharing|51051452|7b22746f6b656e223a227832554930463732386747654672552b396e2b56374b46545a5a4331755077456552346441524952736c593d222c22746f6b656e5f76657273696f6e223a225632227d}} - {{Ancestry Record|2380|13396}} (accessed 20 December 2025)<br/>Clerk's Name: Richard Ellwood; Clerk's Father: James Ellwood; Attorney: Henry Dixson; Filing Date: 10 Nov 1791; Parish or Town: Castle Sowerby; County: Cumberland.