I called
01452 366292, listed in the database: A recorded message said that "We are sorry but due to circumstances beyond our control we are not able to answer your call, sorry for any inconvenience, please try again later."
I then called
0114 203 3183, listed in the database: A chap answered, saying Job Centre Plus (I thought that's good) but after I explained I wanted advice re my existing claim, he asked me where I got the phone number! I reeled off the usual about how my phone is banned from calling 0845's, 0844's, etc and to my surprise he said that he shouldn't really transfer me, but he did.
I was pleasantly surprised that he transferred me to the correct branch, but I strongly suspect that 99% of the time he/they tell people they can't transfer.