A very strong gut feeling and clues from here and there suggest to me that his birth is the one registered in Barton Regis district Q3 1882, His RN record gives his place of birth as Westbury Wilts but, as suggested earlier, I believe the RN got the county wrong, there are no Edward Leach births in Wiltshire that year. He gives his birthplace as Bristol, Westbury on Trym is a suburb of Bristol and was then in the Barton Regis registration district. There are a number of Leach families in Westbury on Trym in 1881. There were a good number of Industrial Schools (boarding schools for poor and neglected children) in that area including including the industrial school ship Formidable at Portishead from which many boys would join the RN (he is not there in 1891).
Only the birth cert would prove/disprove this however but for what it is worth................
maxD