You firstly start off by applying online. You will then be sent a strengths based online test. It takes about 20 minutes to complete. Once completed you'll be sent a skills review of what your strengths and weaknesses are. I had to email to see whether I passed or not, luckily I did, you should get a reply within 24 hours.
You'll then be invited to a video interview done over Skype. The interview isn't conducted by BT, it's an external company due to the amount of applicants. The video interview only takes roughly 15-20 mins. Pretty basic questions, the only one relevant to BT "Why do you want to work for BT" and "Why specifically did you choose your degree".
If you've passed this you'll have to complete a coding exercise within a week. It will have some ambiguity in the brief, so expect not to be told everything. Just do what you can!
Now if you're at this stage, you've done pretty well. The final stage is an assessment centre. Try and get on the earliest ones possible as positions fill up pretty fast. The assessment centre is split up into 5 tasks. A VR Test (This is really fun, no prep needed), A strengths based interview (More in depth, a bit like the Skype one), A group exercise (Solve a problem with everyone else), A technical interviews (They run through your code and you also complete a weird sorting problem) and finally a presentation kinda exercise (You'll read instructions on how to do something and then you'll present it back 1 to 1). Overall, the day is really relaxed it's run by mainly graduates so you won't feel under pressure and you can perform to the best of your ability. You're NOT in competition with others so don't try and dominate everyone in the group exercise. Best of luck :)