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| Date from | Date to | Event | Source |
|---|---|---|---|
| 1726 | Passed the Lieutenant's Examination | RNLPC | |
| 16.12.1732 | Lieutenant ADM 6/14/192 | CSORN | |
| 7.9.1741 | Commander ADM 6/15/451 | CSORN | |
| 7.9.1741 | 8.10.1742 | Thunder (8), Commander and Commanding Officer ADM 6/15/451 | BWAS-1714 |
| 9.12.1742 | Captain ADM 6/16/282 | CSORN | |
| 9.12.1742 | 30.4.1743 | Lark (40), Captain and Commanding Officer ADM 6/16/282 Commission confirmed 28.3.1744 | ADM 6/16 |
| 1.5.1743 | 18.7.1743 | Thunder (8), Commander and Commanding Officer ADM 6/17/25 Commission confirmed 22.11.1745 | ADM 6/17 |
| 19.7.1743 | 10.11.1743 | Lichfield (50), Captain and Commanding Officer ADM 6/16/282 Commission confirmed 28.3.1744 | BWAS-1714 |
| 11.11.1743 | 13.9.1745 | Cumberland (80), Captain and Commanding Officer ADM 6/16/517 Commission confirmed 23.7.1745 | BWAS-1714 |
| 9.4.1754 | Appointed Knight Bachelor | ODNB | |
| 1755 | 1756 | Appointed High Sheriff for Oxfordshire | ODNB |
| 15.10.1755 | 20.8.1756 | Jersey (60), Captain and Commanding Officer ADM 6/18/213 | ODNB |
| 20.8.1756 | 29.11.1756 | Hampton Court (64), Captain and Commanding Officer ADM 6/18/302 | ADM 6/18 |
| 3.8.1757 | 18.12.1760 | Royal Anne (100), Captain and Commanding Officer ADM 6/18/425 | BWAS-1714 |
| 21.10.1762 | Rear-Admiral of the Red ADM 6/19/445 | CSORN | |
| 7.1763 | 1767 | Dreadnought (60), as Flag Officer, Rear-Admiral of the Red | BWAS-1714 |
| 14.7.1763 | 1766 | Appointed Commander-in-Chief — Jamaica ADM 6/19/520 | HJ-DB |
| 31.10.1767 | Created 1st Baronet Burnaby of Broughton Hall | EWIKI | |
| 18.10.1770 | Vice-Admiral of the White ADM 6/20/302 | CSORN | |
| 24.10.1770 | Vice-Admiral of the Red ADM 6/20/305 | CSORN | |
| 1771 | Appointed Commander-in-Chief — Jamaica | ODNB |