We faced a similar problem in a client organization where lack of English fluency was hurting the careers of a team of technical associates but despite push and training programs from the HR, they were not serious about building English skills.
Turned out, the problem was not that they didn't know how beneficial English could be to their growth. The problem was that they had accepted that they will never be able to really improve their English and all the training etc was at best, an amusing time pass.
The solution lay in educating them in how, speaking good English was a skill like driving or swimming which can only be perfected by lots and lots of practice. When backed by training modules that focused on personal interaction in low anxiety situations, the team really latched on to the training. Engagement, attendance and training performance were way ahead anything that had ever been achieved by any training program.