Starting at Uni is daunting and it may or may not be the course, but the whole change from home & school you're struggling with. Talk it over with a counsellor at Uni and clearly articulate what course you want to do, why you want to do & why you're passionate about it. Try to fathom what it is that is triggering your anxiety...wrong course...wrong uni...wrong time to leave home?
Don't worry about the age thing, I did a year at college so went at 19yrs old and the year was negligible. I did my first two years then took a break before going back at age 23 to finish my final two years (honours degrees being 4 yrs total in Scotland) and that was a wee bit different age-wise but you still find people to click with. So don't let that make you feel different....lots of people have gap years, or decide their first year was not right for them, you often can still get funding to complete your course.
I'm looking at the grand old age of 43 to be starting a PG course, and everyone else will be approx half my age but I'll swallow the discomfort as I'm passionate about my course.
Your parents need some commitment from you that you will go back, and applying now for next year will show that. Have a plan and realistic goals for your year out (not just "I'll get a job" - job market not great, so show what job area you're looking at & applying to) will appease the parents and show you're not just taking the easiest route...parents worry about you, it's their job and they want the best for you and them. Don't make them have sleepless nights worrying about you and your future....they will support you, but be decisive and forward planning with achievable goals and they can rest easier. Good luck! Gx