Probably the Cornelius Neech referred to in the A2A website at http://www.a2a.pro.gov.uk/search/docframe.asp?~styletype=xsl&i=3&stylesheet=xsl\A2A_com.xsl&com=1 as follows:

MEADE OF EARSHAM

Earsham

FILE - Deeds of western part of a dwellinghouse with shops etc. ( rooms named) on Earsham Street and Church Lane sold by Mary Girdlestone widow (who retained the residue) to Jonathan Baker in 1838 - ref.  MEA15/7, 692 x 5 - date: 1838-1901 [from Scope and Content] In 1853 Cornelius Neech purchased from Baker and in 1879 he sold it (described as a dwellinghouse and two small shops) to George Fisk.  Fisk's executors sold it in 1901.  Documents include Abstracts of Title from 1776, mortgage deeds, plans in conveyances of 1838 and 1853, sale particular 1878, and billhead 1892 of Stanley Fisk plumber and house decorator of Lavenham. 

Source : Robert Neech Family Tree from Evalyn.  Family Tree from Alan Neech.