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The only Jewish cemetery in the area would be West Ham, Buckingham Road Forest Lane, E15 opened 1857, there is another known as Plashet, High Street North E12 but that did not open until 1896.  The names are very English and I suspect William is an adopted name, Goodman was probably anglicised the children might have been registered under a different name, it was not uncommon for Jews to change their surnames.  What is unusual is for the son to have the same given name as his father it is not an Ashkenazi (Central or Eastern European Jewry) custom to name after living relatives although Dutch Jews did.  If you can get a photo of the graves and get the Hebrew translated it would give you more clues.  Going by their names this seems to be a family who wanted to assimilate I would be surprised if they did not register the births of the children.  The reasons for some Polish and Russian new emigrants not registering births & marriages, was fear of "the authorities" mainly due to long term army often 20 years or more conscription of Jewish males and old habits and suspicion of authority is hard to break.  It was not unknown for Jewish marriages to be restricted in some parts of Russia and Poland.

Thank you for your reply, Interesting that you think Emma/Hannah is Phillips Mother.  I need to do some deep digging,   There is information about Pricilla, the name was passed down in the family, one of the sisters Elizabeth nee Hart who married Abraham Lee called one of her daughters Pricilla.  This is my maternal line so really interested.  The GRO cross checking facility is really a life saver.