My Great Grandma had to leave Russia when she was just 16, and travel to England. I know the ship she took from England to America, but I don't know how she got to England. Would it have been the same ship?
When you say you know the ship, do you mean you know the ship's name or have you seen the passenger list (image)?
The passenger list page headers in that period should have originating port information. It may show that that ship's voyage started in England or it may show another European country, not necessarily Russia. It is possible that your ancestor made her way to Germany or Scandinavia or even further, overland (trains) or by sea (even multiple short trips, but most likely just 1).
If her voyage originated in England or she got on board in England, it is possible that she stayed in England longer than just the time to change ships.
There may also be pages that the start of the transatlantic voyage's record with general information. Researching the ship may tell you its usual ports-of-call.
Note that "local" passenger lists (from Europe to England) were usually not retained.
As per https://genealogy.stackexchange.com/a/15574/6485, European emigrants to America via England usually landed at an East Coast port (most often Hull or Dover) and took a train to a West Coast port (e.g Liverpool) to take a ship to America.
So it is unlikely that your Great Grandma stayed on the same ship throughout, and you should follow the advice on the linked answer.