Stephen,
Don't necessarily give up - try a bit of lateral thinking. First of all try to get this picture. From c.1795 until 1919 Central and Eastern Europe was divided up between the three great Empires - German, Russian and Austro-Hungarian with Poland split between the three. This meant that people could be German, Jewish, Polish, Lithuanian, Czech, Slovakian by ethnicity - speak those languages at home but be either "German, "Russian" or "Austrian" by nationality. so if they were stating where they had come from, travel documents etc., they would say "Russia" for example.even if they were Polish.

Now, if you take a look at the 1901 and 1891 censuses under Mark Smith you will find the family at different addresses in the East End - father working always in some sort of iron trading, daughters tailoresses etc - pointing to the fact that they could have been Jewish, but where they state that the place of birth was Poland (obviously the bit that was "Russian") Look one further back and they do not appear on the 1881 census - well they do actually. Mark SCHMIDT plus family, born in Poland, is living in St. George's in the East - still working with iron in some form. The 1871 Census does not show the family at all. This points to them being German speaking, probably Jewish, coming from Poland, the bit that was Russia sometime in the 1870s - all the children seem to be British born, but he obviously got fed up with being Schmidt so just used the English version - Smith. Don't forget that one can/used to be able to use any name one wished in England as long as the change was not intended to defraud so he would not have had to do anything formal to say he was Smith, not Schmidt. You might ask if the London Metropolitan Archives has any suggestions where you might get more information or, as there seems to be an indication that they were Jewish why not try JewishGen? but don't forget he was Schmidt when he came and at least it has narrowed down to being the bit of Poland which was Russian. Enough for tonight. Good luck...