This is the EXACT wording on the baptismal entry,
feb 15th 1829 number 290
Ann dr of - Baseborn
Harriet Wakeham
Amberley
Servant Incidentally you listed the 1841 census for Rackham rather than Amberley. I mention that because there was no obvious reason why Ann should be living in Rackham as she was from Amberley. It would infer that she had family there.1841 - HO107/1092/1/7/6 It is Amberley, it states, 'Amberley hamlet of Rackham'
As we know her mother had died around 1837 Harriet, Ann's mother died 1833 age 23 (dob 1810)
Thomas Gent disowned her as he wasn't her real father. We don't know that Thomas even knew about her existance. We do know that Thomas didn't keep his legitimate son with him

Perhaps we can find out who this PESCOTT/PRESCOTT couple are.
Broadwater, West Sussex, 17 Feb 1829:
Margaret FORD
Bernard WEST, botp (B)
Witness wit: Eliza FORD; Henry WEST
Looks like Bernard & Margaret stayed in Broadwater for a time then by 1841 they are back in Amberley.
1851 shows Bernard & new wife, Mary in Broadwater again. Jane is a servant in the household of George & Francis Haines at 6 Warwick Buildings, Broadwater,
Jane West serv. unm. 19 b. Rackham.
The JANE WAKEHAM bit is a red herring I'm afraid. Barnard's daughter Jane was born in Worthing in 1831 as were the first 3 children. I have Jane living in London in 1861:-
Census 1861: 24, Dorchester Place, St Marylebone | Jane West | 29 | Sussex, Worthing. I think you're right. This Jane is unm, laundress with a 3 year old daughter, Amelia born Brighton.
A John Wakeham married a Sarah Braby on 19th November 1816 in St Michael's, Amberley. I don't know whether they were the parents of Jane Wakeham, but it might explain why she was living in a Braby household.I had also spotted this on the SMI,
Amberley, West Sussex, 19 Nov 1816:
John WAKEHAM, botp
Sarah BRABY
Witness wits: William WAKEHAM; Jane WAKEHAM
From the IGI extracted record they had Charles Wakeham Amberley, 1818.
On the SAME DAY,
Amberley, West Sussex, 19 Nov 1816:
William WAKEHAM, botp
Jane HOPKINS
Witness wits: Frank FARED; Robert BRABY
Looks like two brothers having a double wedding! I think they are the sons of John & Susanna Wakeham (nee Coote) married Amberley 1789.
jane