I'm following up on Rimmers of Formby/Altcar at the moment, as this is the family of my GG grandmother, though I also have numerous Rimmers cropping up elsewhere in my Southport (North Meols) tree. So far, I have traced back to Thomas Rimmer, Farmer, born c1775-81 (no definite birthplace). He married Alice Whitehead in 1797 with whom he had children Thomas, Catherine, John, James, William, Richard, Ann & Henry. Thomas later married Elizabeth (unknown), probably around, or shortly before, 1828 and had sons Joseph & George. Thomas Died before the census of 1851.
His son, James (1804) married Jane Aspinwall of Halsall and they had 3 children in Formby before moving to Toxteth Park, where my GG grandmother, Margaret Rimmer, was born.
As for the origin of the family... they are mostly from the Southport (formerly North Meols) & Birkdale area and by the earliest church records of the late Tudor period there are many of them in the district (though no indication of them 200 years before at the time of the Poll Tax in 1381). The name means from the "Rim of the Mere".
It has long been by far the most common name in the Southport area.