British names like jones, Adams , smith are completely different from all other cultural influences in England.
Also- does anybody know what happened to anient brittonic/Celtic surnames??
I'd like to challenge your starting assumption.
using the Wikipedia entry it says the most common surname in England is "Smith" - The second most common surname in Germany is "Schmidt", well actually all spelling variations taken together end up being the most common name. And it's the same name. Let's go down the list a bit. Number three on the list is "Taylor" which translates to "Schneider" - conveniently Schneider is also the third most common surname in Germany. The most common name in German is "Müller" which would be "Miller" in English. It doesn't seem to make it that high on any list, but it's definitely a name that exists in England.
A lot of other names are variations with "-son" Wilson, Jonson, Robinson, Thomson, Jackson all make the top 20. Now this has no equivalent in Germany. Names of that kind do exist (e.g. Jansen - son of Jan) but are less common. However that naming is by far the most common in Skandinavia. Pretty much every name on the List for Norway ends on -sen and the Swedish ones on -son.
So basically surnames in England are not that different than surnames in Germany or Scandinavia. Looks like they went through similar processes of origin and adoption than the rest of Europe, mixing different methods.
Surnames are a (relatively) recent invention, adopted in the 13th and 14th centuries. It was not until Henry VIII that it that birth records were required to be recorded using the father's surname.
Many English surnames were thus spontaneously adopted at one point or another. Often before the incidence of surname use it was sufficient to refer to someone as John of Place or John, son of Person. This explains the lack of obviously Latin, Germanic, French etc surnames - the words were derived from English words, names and locations.
As for Celtic surnames, the lack of widespread use of surnames before the late medieval period explains why they don't really exist in England, but there are plenty of obviously Welsh, Manx and Cornish-derived surnames knocking around in the UK.
Given the large proportion of English people with Irish ancestors, there are a fair number of people with clearly Gaelic names that take the form O'(something), derived from the Irish for 'son of'. Similarly with the Scottish Mac(Something)