It turns out the text I received was genuine.
All I can say is whoever at BT/EE decided that someone should click on a link within the text and then have to enter their email and p/w to log in to get the code is a total idiot. I didn't enter any of my information but after EE and BT have both assured me that the text I received was genuine (I forwarded it to EE). So now I've entered the competition from the text they sent me.
I doubt they'll get many people entering the competition if they leave it as it is, but there may be some people who still click on the link, thinking it's genuine, which of course it is, and those people are likely to fall prey to scammers with similar scams.
Very irresponsible of BT/EE to send out those texts to their customers.
