Phone issues, trying to log in....

So, basically, new phone, new number. Old phone has several issues. I tried to log in to my Universal Credit account - they DO have my email address and when I have an appointment, I get a text AND an email. I can NOT use my phone (battery is very low, not charging AND the sim card is stuck, even the phone shops could not help.
I know I can phone them, it's annoying having to phone from work but what can I do. But I've heard sometimes people have to go into the job centre. I have started working, which they know and I will update them after I get paid about that. It's on the other side of my city too & the other side of my city from the job centre. Is there ANY way around this? Like I said, they DO have my email address which they also use but on the log in page, I can't see any option to be emailed the code, it's saying to phone if I can't get the code.

I don't mind phoning but I just REALLY don't want to have to take a day off work over this to have to go into the job centre with 3 forms of ID when they have my email.

The reason I was trying to log in was to say I have a new number & update my profile with what it is.

HELP!