It looks as if Elizabeth had another son, Timothy, also baptised the same day. Both boys are indexed under Newnham and Meadhurst.
There is a marriage for Elizabeth Newnham to John "Midhurst" in Brighton 14 March 1803 but I can't think why the boys would be called Newnham if they were from that marriage. If possible you need to look at the original registers to see if they hold any further clues.