Finding immigration records is generally pretty tricky. If they came from Odessa, it's hard to say how which route they took. Have you tried looking on passenger lists for ships from Hamburg that were bound from to the USA?
I found the following birth registration on the GRO site:
GORAVITCH, CELIA MARKUS
GRO Reference: 1907 M Quarter in LEEDS Volume 09B Page 414
GOROVITCH, EMMANUEL MARKIS
GRO Reference: 1908 S Quarter in LEEDS Volume 09B Page 401
GOROVITCH, HERMAN MARKUS
GRO Reference: 1910 D Quarter in LEEDS Volume 09B Page 269
GUREVITCH, LEAH MARCUS
GRO Reference: 1914 M Quarter in LEEDS Volume 09B Page 682
GUREVITCH, MAX MARKOS
GRO Reference: 1917 S Quarter in HULL Volume 09D Page 374
By the looks of it, Emmanuel was indeed born in Leeds.
There is a family tree on ancestry owned by a Paul Gurevitch, which includes these five siblings as well as 3 older siblings (b. Leeds) and a younger sibling (b. Hull). The parents were reportedly Hyman Gurevitch (b. 1876 Russia, d. 18 Oct 1919 Hull) and Martha Betsy Marcus (b. c1888 Riga, d. Sep 1935 Hull). The Jewish surname Marcus indicates a German language influence, which fits with the suggestion that Martha came from Riga.
The family was in Halifax in 1911. Hyman's 28-year-old brother Judah was living with them. Look under Hyman Gurevritch.
It's always worth while checking if there is a realistic family tree on ancestry. This one appears to be one.