It all looks to be outside Sussex for John died in Lewisham in the June quarter of 1888 (ref 1d 586).
You can apply for a copy of his death cert from the GRO giving the above reference.
1881 census has him as born Pimlico, London,
wife from Leeds and children born Bristol & Southport, but no Sussex conection.
1858 he was in Leeds to marry Sarah Mawson,
1820 he was baptised in Westminster.
Siblings 1815 - 1835 Henry, Eliza, John Hussey, William, Thomas & Mary also baptised Wesminster (IGI Batch Number: C041601)
No trace of the Harvard-Hussey marriage but a Hussey enclave is known to have existed in the Basingstoke area of HAMPSHIRE.
1789 marriage to Mary Otley in Brixton, & baptism Shoreditch 1788 (IGI).
Sister Mary Ann born Bristol 1797. (IGI references are unsubstatiated so you need to verify that Bristol has not been mistranscribed as Brixton or vice vesa)
You also need to see a copy of the above marriage entry to see if it gives John's parents as John & Lydia or James & Jane, for there are two London baptisms (1758 & 1763) and either of them could be him
Perhaps that might put a bit of meat on the bones of what you have already and if there does turn out to be a family link to the John Harvard who started the American University of that name, the Sussex connection will probably be that on April 19 1636 John married Ann Sadler (b. 1614) at South Malling. Ann was the sister of the Reverend John Sadler, Vicar of Ringmer.
By the way, the same university document that the above information came from suggests that John Harvard's London based parents and most of his siblings were wiped out in a London Plague of 1625, and his last surviving brother died in 1637, leaving John to inherit the entire Harvard estate. However, unless 1625 marked a lesser plague, I had always understood the great plague to have been about 4 decades later in 1665!
Roy G