I cannot find a William PLUMMER/PLUMBER aged around 20, born Ixworth on the 1851 Suffolk Census Index. I also cannot find a William PLUMMER/PLUMBER living at Ixworth in 1841.
I did find a William living at Ixworth on the 1871, aged 39 with wife Jane, and children Sarah, 10, Willie, 6 and Walter 4. But this doesn't seem to marry up with the 1881 entry.