Excellent, Anne. We now know that the Woodcocks weren't in ownership when the building was rebuilt and we have a rough date for the road widening, 1775.
By Reader I assume it means William Reader, not articles written by readers, although there were quite a few of those on Coventry history and buildings.
From wikisource his works are:
1. 'An Authentic Record of the Lammas Grounds belonging to the City of Coventry, from the original record by Humphrey Wanley in the British Museum,' 1810, 12mo.
2. 'A Description of the Churches of St. Michael and the Holy Trinity, Coventry,' 1815, 8vo.
3. 'The Charter granted by James I to the Mayor, Bailiffs, and Commonalty of the City of Coventry in 1621,' 1816, 8vo.
4. 'New Coventry Guide, containing the History and Antiquities of that City,' Coventry [1824?], 12mo.
5. 'The History of Leofric, Earl of Mercia, and his Countess Godiva, from authentic records, with the Origin and Description of Coventry Show Fair,' Coventry, 1827, 18mo; 2nd edit., 1830, 12mo; 3rd edit., 1834, 8vo.
6. 'A Guide to St. Mary's Hall, Coventry,' Coventry, 1827, 12mo.
7. 'Persecutions at Coventry by the Roman Catholics from 1380 to 1557,' 1829, 8vo.
8. 'Description of St. Michael's Church, Coventry, with Inscriptions from the Monuments,' Coventry, 1830, 12mo.
9. 'Domesday Book for the County of Warwick, translated, with a brief Dissertation on Domesday Book, and Biographical Notices of the Ancient Possessors,' Coventry, 1835, 4to; 2nd edit., with brief introduction by Evelyn Philip Shirley, Warwick [1879], 4to.
10. 'A List of the Bailiffs, Sheriffs, and Mayors of Coventry.'
Reader published in the 'Coventry Mercury' many articles on the ancient and modern history of the city; he was an occasional correspondent of the 'Gentleman's Magazine' from 1809 to 1852; and he also made some contributions to the 'Collectanea Topographica et Genealogica.'
The records might be from a mix of these or there may have been others. A lot of old stuff has been lost over the years.