That's quite surprising to hear from them. I would suggest sitting down with your parents and discussing this, and explaining that particularly in first year, you won't have a long term permanent place to stay.
Usually halls contracts are only for the academic year, and at some unis (Oxbridge) you need to actually full move out of your accommodation during the breaks. Also it's typical for students, especially in first year, to plan to go home during the breaks anyway - it would be impractical to bring everything with you every time. Additionally worth pointing out to them even after first year, student rentals in the private sector can be quite varied and usually students will only stay there for a year or two. It would make things much more expensive to bring everything with you while moving multiple times in the span of just a few years.
While obviously storing it in a paid storage depot is impractical and not recommended, is there a reason they aren't happy for you to keep your things in your room at home? Are they planning to immediately remove all the furniture and your things in there when you move out? As they may need to manage their expectations in your moving out anyway as above. Going to uni for a lot of students doesn't mean you've "left the nest" and will not be returning except for short visits...