Would age affect my application?
Your age itself, no (you meet the minimum requirement and it's illegal to discriminate on the basis of age). However, you may also get what I got when I first applied for ATC, straight out of uni (so a couple of years older than you are now): the feedback after my interview was basically to go away and grow up a little, then come back in a few years.
So I went away and worked in the 'real world' for a bit, took on a job that allowed me to demonstrate responsibility, and three years later was successful.
Having said that, that was my experience, yours may differ. Give it a go, and try not to get too disheartened if it ends in tears the first time.