My IT corporation considers learning new things as crucial part of their competitiveness. So out of 8 hours of daily working time, we are expected to work 7 hours on projects and have 1 hour for other activities, especially
- learning new things
- preparing for certifications (what is learning things, too)
- administrative tasks
Employees determine what they want to learn by themselves, but of these things, some are always consulted with the manager and officially recorded as commitment to individual's career development path, which is tracked and evaluated.
We are also encouraged to hold one hour per week as meeting for the whole team (where presence is expected, but not mandatory) on teaching others new things we learned.
So in the summary, 5 out of 40 weekly hours are available and paid for this. If I don't have time to follow this for longer period (project work is going 40 hrs/week), I am raising this with my boss as an alert, because development goals are going to be missed.
You can check with your manager and maybe give them the above as counterexample how some companies in industry do this. It is in company's own interest to provide time for learning.
Your manager's reaction is one of results of the test whether your employer is worth you, because if you imagine staying there and losing the opportunities (when compared to other possible jobs in the industry which you could work at) it can be a deal-breaker. Of course, alternatively you can try a 'partisanship', learning things on your own, gaining advantage against your colleagues who are not. Maybe this can accelerate your career in your current company, maybe not (if they are not valuing these skills enough). Anyhow, sooner or later you will see whether to stay or go.