Should I be worried about the fact that I don't have any experience since my CV states that I haven't got much experience in programming , HTML especially?
Since you will be starting an apprenticeship you should not worry about this. That is the whole point of being an apprentice: to learn about the subject. The good thing about this is that after you finish your apprenticeship you will be able to include that in your CV, further improving your changes of getting jobs related to the subject.
The person who hired you is most certainly aware of this, otherwise they would have hired or contacted someone who already knows how to work with that technology. So there is no need to worry about what they will think of you.
Could you give me some advice how to learn the language faster?
There is an Italian saying:
Chi va piano, va lontano - He who goes slowly goes far
That is, take it easy, don't bite more than you can chew. Give time to your learning process, at first it may be the case you feel stuck or that you are not getting better as fast as you expected. This is normal at the beginning, so don't get disappointed if you find yourself in this situation.
If at some point you really feel stuck don't hesitate and ask for advice; not knowing something and asking is a sign of maturity and willingness to learn, so there is nothing wrong in asking. Make sure you take advantage of the knowledge other more experienced coworkers happily share with you and you will lean faster than having to bang your head with every wall you find. Good luck with your apprenticeship, I hope these suggestions help you.