Uriah Moses (1780-1847) was transported from England to Australia in 1800. Fortunately his trial for theft was at The Old Bailey and the detailed trial notes are available online. Uriah's life, initially as a convict and then as an emancipist in Australia, is relatively easy to trace however searching for information about his life and that of his family in England is more of a challenge.
A good place to start is FamilySearch which provides a detailed section in their wiki on researching English Jewish Records. This includes a useful summary on the history of Jews in England.
The Jewish section of Cyndi's List also has links that may be useful. Searching by location (England) within this list leads to the British Jewry website.
In the trial notes Kitty Jacobs is called as a character witness for Uriah. Online searching suggests that Kitty Jacobs was Kitty Moses before her marriage. A general Google search for Kitty Moses and Henry Jacobs
provides links to a variety of sources which may, or may not, be
helpful. One link is to a section of a book, Wealth and Notoriety: the extraordinary families of Lawrence Levy and Charles Levy,
by Robert Ward which includes information about Rebecca, a daughter of
Kitty and Henry, marrying Lawrence Levy. Searching for information on
other children may also be useful. An entry in WikiTree provides some information about Kitty and her family.
The website, Synagogue Scribes, provides a database of London Ashkenazi Synagogue records, with the emphasis on pre-UK civil registration. In this database is a record of the marriage of Kitty Moses to Henry Jacobs at the Great Synagogue in 1793.
British Genealogy and Family History Forums has a section on queries about the name Moses Cohen / Moshe Cohen. There is also discussion on this family on this forum page (towards the bottom of the page). References in these notes are made to Jacobs Tree website.
Another British Genealogy forum with relevant posts.
Cemetery Scribes could also be a useful resource.
What was it like to be Jewish in London at the end of the eighteenth century?
The Great Synagogue was the place of worship for Ashkenazi Jews in London. Synagogue Scribes has some brief information plus an image of the Great Synagogue. Further information about the synagogue can be found in Family Search. There is also information about the Great Synagogue in the Susser Archive.
The Great Synagogue was founded by Ashkenazi Jews. Recent research using DNA suggest that these were largely from European families who had converted to Jewish religion (Live Science 8 October 2013).
Many were from Germany and other Western European countries. Additional information can be located in another article in The Scientist 8 October 2013.
There are a number of online sites which may provide useful background information about the Jewish community in London at the end of the eighteenth century and early nineteenth century.
The Jewish Virtual Library has an article on Ashkenazim and another on Jews in the UK.
Old Bailey Online has an article on Jewish communities and also on London from 1760-1815.
As it is believed that Uriah was born in Exeter in Devon it is necessary to look at the Jewish community in that region.
Wikipedia has an article about the history of the synagogue in Exeter which was consecrated in 1764. The synagogue is located in Synagogue Place, Exeter.
A book by Helen Fry - The Jews of Exeter - has been written about the history of the synagogue and was published in 2013.
A paper on Multi-Cultural Exeter 1500-1800 is also available online. It also includes a reference to the book - The Jews of Devon and Cornwall published in 2000. Lists of the names of Jewish families from Exeter appearing in the 1841 and 1851 census are included.
Exeter Memories has a page on the Jewish Cemetery in Exeter. There is also a page on the Exeter Synagogue.
Rabbi Bernard Susser wrote a thesis on Jews of South West England (1977) which is available online on the JCR-UK website.
As I work through these resources no doubt other useful links will also be located. It is unlikely that the links will provide answers to all the questions that will arise but at least they should help in providing a better understanding of the life that Uriah may have had as a Jew living in England.