His father, also named Richard, was a Cheshire man, who settled in Liverpool early in life, and died there on 15 June 1852, at the age of 91.
He particularly focused on exploring fields of battle in England, especially those which were the scenes of conflict between the rival houses of York and Lancaster.
Brooke's primary research goal was to compare the statements of the historians with such relics as had survived and with the traditions of the neighbourhoods where the respective battles had been fought.
In 1825 he published Observations illustrative of the Accounts given by the Ancient Historical Writers of the Battle of Stoke Field, between King Henry the Seventh and John de la Pole, Earl of Lincoln, in 1487, the last that was fought in the Civil Wars of York and Lancaster; to which are added some interesting particulars of the Illustrious Houses of Plantagenet and Neville (Liverpool, 1825, roy.
The battlefields described are Shrewsbury, Blore Heath, Northampton, Wakefield, Mortimer's Cross, Towton, Tewkesbury, Bosworth, Stoke, Evesham, and Barnet.