Lyme Regis is a hot spot for ammonites.
From the age of the rocks thereabouts, we can gauge the age of your specimen to be lower Jurassic (roughly 189-199 million years old) or lower Cretaceous (roughly 102-106 million years old).
Somebody with local knowledge may be able to hazard a guess at the genus, but that's not me.
Looking mainly at 004.JPG, the other pieces are mainly fragments of ammonites (not necessarily the same one). They may show different curvatures depending on the part of the animal they came from, and depending on how much they were cracked and deformed during burial. The most obvious ammonite fragment looks almost like an armadillo's platy skin due to fracturing. Other pieces could be aptychi (see last ref. below). There is also a mould of part of a bivalve(?) shell.
- Discovering Fossil's page on Lyme Regis - http://www.discoveringfossils.co.uk/lyme_regis_fossils.htm
- Ian West's page on The Fossils of the Lias, at Lyme Regis, etc. - http://www.southampton.ac.uk/~imw/liasfos.htm
- aptychi - http://en.wikipedia.org/wiki/Aptychus