| RefNo | Title | Date |
| EC/1740/07 | Davall, Peter: certificate of election to the Royal Society | 23 October 1740 |
| AB/1/2/1/20 | Order that Peter Davall advance £50 to Reverend Maskelyne out of the money lately granted to the Society by his Majesty | 14 July 1760 |
| AB/1/2/1/54 | Peter Davall's Account with the Royal Society | July - October 1762 |
| AB/1/2/3/28 | Receipt for interest on Royal Society's stock received by Hauksbee from Peter Davall | 23 April 1760 |
| AB/1/2/1/29 | Mr Davall's account with the Royal Society | 29 November 1760 |
| AB/1/2/1/31 | Receipt for £51 received from Peter Davall being half a year's dividend on £3400 three per cent Bank Annuities by Francis Hauksbee | 17 August 1761 |
| AB/1/2/1/48 | Letter to Mr Davall from Mr Rucker advising him that he has settled the Exchange of the Bill with Mr Berens | 23 July 1762 |
| AB/1/2/1/30 | Mr Davall's account with the Royal Society | 29 November 1760 |
| AB/1/2/1/50 | The Council of the Royal Society Debtor to the Reverend Nevil Maskelyne | 1762 |
| AB/1/2/1/21 | Receipt for £45 received from Mr Davall for half a year's dividend on £3000 being the Royal Society's stock in the three per cent reduced annuities | 19 October 1760 |
| AB/1/2/1/55 | Unsigned copy of Peter Davall's Account with the Royal Society | July - November 1762 |
| AB/1/2/1/26 | Bill for John Dollond | 19 December 1760 |
| AB/1/2/1/24 | Order of Council to Mr Peter Davall to pay Mr Robert Waddington or the bearer the sum of £35 out of the money belonging to the Royal Society in his hands | 20 November 1760 |
| AB/1/2/1/28 | Order of Council That Peter Davall Esq, VP pay into the hands of the Treasurer, the Balance now remaining in his hands of the money received by Him at the Exchequer in consequence of his late Majesty's warrant | 21 January 1761 |
| MM/3/92 | Letter from de Saint Jacques Silvabelle, Marseilles, to Peter Davall | 16 January 1752 |
| AB/1/2/1/47 | Bill of Nevil Maskelyne | 21 July 1762 |
| L&P/2/392 | Letter, 'On M. Daran's bougie having been anticipated (with letters from John Ruding (surgeon) and a patient. Thomas Reynolds' from James Wallace to Peter Davall | 21 December 1752 |
| L&P/2/531 | Paper, 'An account of J Robertson's 'Elements of navigation'' by Peter Davall | 1754 |
| L&P/2/428 | Letter, 'Of Baulinia seeds' from Philip Miller to Peter Davall | 3 March 1753 |
| AB/1/2/1/45 | Letter from Peter Davall to Dr [Charles] Morton at the British Museum | 2 July 1762 |
| MM/10/123 | 'Account of moneys apportioned for 29 November 1760 for the expenses of the observations', by Peter Davall | 22 July 1760 |
| EL/D2/50a | Note on Monsieur de Lisle's [Guillaume Delisle] paper which compares the magnitude of Paris with London and several other cities by Peter Davall | 1725 |
| EL/D2/50 | Letter, from Peter Davall to William Rutty, dated at Temple | 19 June 1728 |
| MS/790/32 | Letter from Peter Davall, Temple, to Martin Folkes | 18th century |