According to The Place Names Of Wiltshire (English Place-Name Society Volume XVI) by J.E.B. Gover, Allen Mawer and F.M. Stenton, published by Cambridge University Press, 1970:
Emwell Street (6″). Cf. Emewell 1249, 1394 Assize Rolls for Wiltshire (Public Record Office), Emewelle 1332 Lay Subsidy Rolls unpublished, Emwell 1344 Calendar of Inquisitions Miscellaneous, Calendar of Close Rolls, 1348 Calendar of Patent Rolls, Emwell al. Emble Coppice 1650 Parliamentary Surveys, Public Record Office. The forms are too late and indecisive for any etymology to be suggested.