I cannot share all that you have gone through and are experiencing now, but just to add another snippet which may help.
If you feel your own GP may not be the most supportive in this matter - and not every GP is because they may not have that ability to empathise as we would hope - then ask your surgery if any GP there is the Lead Mental Health and if so, can you get to see them.
If they have any nurses attached to the practice, they may have one who is trained in counselling for the bereaved, or the GP you see may be able to refer you to a counsellor for sessions to help you cope with this.
Follow the advice here about making a complaint to the DWP, and if you cannot get the help you need from your GP in time before you have to attend the interview at the cancer centre, try and find someone who can at least go with you to the door and wait until you come out again so you are not unsupported, and you do not end up sanctioned.
Good luck and remember it is ok to feel like you are losing it and falling apart. Not having any feelings and just rigidly getting on with life is not the norm nor is it healthy. Eventually you will learn to feel better, but in your good time, not in the time that anyone else can dictate.