I'd not heard of it but I've just taken a look here
https://www.itv.com/comps/competitions/free/267/on_the_2nd_day_of_christmas_itv_gave_to_me_the_chance_to_win_one_of_11_amazon_kindle_fire_7s
and had a crack at it (using Firefox).
I clicked 'Enter Now', on the right of my screen, entered my mobile number and immediately got sent a text with a 4-digit registration code, which I entered on the screen. I was then asked for a 'memorable pass code', which stumped me for a moment as I thought that was what I'd just entered but I then realised that I needed to enter a
different code, of my own choosing (and, as I found, then confirm it on the next screen).
Perhaps you've been trying to enter the first code (which was sent to your phone) there, rather than a different one? If not, how far do you get with it?