Are you in an English speaking country? If not, were you informed in the interview that you'd need to communicate mostly in English? Either way, did you communicate that English isn't your strong point and something you'd need help with?
If you conducted the whole interview process in English, have English literacy on your resume, and/or were told that English is a skill that is required for the job, then yes, it is reasonable for them to say that your written English isn't at a level they need to conduct business.
If it is an issue, I'd approach your manager/boss and say you know it's not your strongest point and say you'd be willing to take some business English classes if need be. If you show you're willing to work on it, and actually show improvement in that area, it shouldn't be as big of an issue.
If you are coming off as 'I wasn't hired on this skill' and being confrontation, then I can understand why you were told it could escalate to more than a verbal warning in the future. It's not the skill that's the issue, it's your attitude of "I wasn't hired for that" that is the issue.