Yes, it's grammatical, and would normally be a polite way to ask for something. However, it's difficult to say whether it would be appropriate for your purpose without knowing more about the situation.
Who told you the second one was "not correct?" I don't think "not correct" is quite the right way to say it.
I think this has to do with the word knowledge more than the word English. When talking about any kind of knowledge, I can see where a textbook teaching formal English would recommend saying:
knowledge of X
or
knowledge about X
over
X knowledge.
After all, in these expressions:
- coin knowledge
- car knowledge
- garden knowledge
words that are mostly known as nouns are being put to work as adjectives. So a textbook might say that it would be better to use, knowledge about coins, cars and gardens.
However, in reality, such nouns are pressed into use as adjectives all the time.
Fact is, the expression English knowledge can be found in published works academic studies, as evidenced by anecdotes found here, here, and here.
However, as Edwin points out in his comment, the phrase "English knowledge" is ambiguous; it can mean knowledge possessed by the English, not knowledge about English, as is the case here.
I would say that knowledge about English might be more formal, or more syntactically precise, but I'd be hesitant to call the other "incorrect."
Best Answer
I can give you the Chinese-language explanation :-)
One explanation:
"my English ability" can be read as "my ability at [doing] things English, whatever they/that may be" (??) :-)
I'd suggest that even:
"my English-language ability"
is better than "my English ability."
BTW, "to improve one's ability in" is idiomatic: