The direct ancestors of Hely Hutchinson Almond are mentioned in this biography.https://archive.org/stream/almondoflorettob00mack#page/4/mode/2up Using that it was possible to get back quite easily to the early 18th C.
Hard at this point to see any possible connection with https://en.wikipedia.org/wiki/Philips_van_Almonde
The biography says that his great grandfather was the headmaster of Derby School . There is a published transcript of their 'registers' online.
Rowland Almond of Northallerton , was father of
Rev. George Almond Head of Derby School c. 1750-61. (father mentioned on Rev George's record at :http://db.theclergydatabase.org.uk/jsp/search/index.jsp ) He was admitted to Trinity, Camb 1728 ( b circa 1710?) He was vicar of Kellington York, 1735-1763, (vicar of Chellaston* Derby, 1758-63? see below )
George married Mary Fox on 25 Apr 1752 at St Peter's Derby).He was buried at St Peters 26 Nov.1763
1)Rowland Almond, baptised, 23 April 1755, at St Peters, bookseller, buried 29 Sept 1787 St Peter's
2)George Almond, baptised 10 June 1755 at St Peter's, (businessman in Leicester?)
3)William Almond, baptised 15 Dec 1756 buried 18 Dec, St Peters
4)Samuel Almond, baptised 24 Nov 1758, buried 29 Nov, St Peters
5)Samuel Almond (appears to be posthumous child baptised 2 Jan 1764
George Almond (son of Rev George) baptised 1755 was a businessman (wonder if the bookselling business with his brother) He was father of
George Almond, who according to the biography was a business man, then a captain of the militia during the Napoleonic wars, then took orders in 1820 and became minister of St Mary's Episcopal chapel in Glasgow.
He was father of 9 children by his first wife
By his second wife, Christina Georgina Smith ( married in 1823) he had two sons,one died in infancy, the other was Hely Hutchinson Almond b 12 August 1832
(baptisms and marriages in Derby, on Family Search)
( * He does not seem to been V of Chellaston. The school register and the extract from Alumuni Cantabrigiensis on the CCED both say that George was buried at Chellaston, and that he was vicar there. There is no actual record of this in his clergy record. The church at Chellaston was a St Peters and at the time was a tiny village with a perpetual curate .
The school register includes the baptismal dates of George and Rowland and the burial date for Rev. George These match the records for St Peter's Derby a different church. "England, Derbyshire, Church of England Parish Registers, 1537-1918," database with images, FamilySearch (https://familysearch.org/pal:/MM9.3.1/TH-266-12872-138263-33?cc=1911752 : 2 April 2015), Derbyshire > Derby, St Peter's Church > Baptisms, marriages, burials 1755-1771 (vol 3) > image 3 of 70; Record Office, Matlock.
puzzling over that took far longer than finding the names of the ancestors as hadn't realised that the images were on FS!)