My guess is Judge Rinder will replace it.
But they could do;
6:00am-9:00am GMB (extra 30mins)
10:00am-12:00pm This Morning
12:00pm-1:20pm Loose Women (extra segment)
1:20pm-1:50pm Lunchtime News and Weather (extra 5mins)
1:50pm-2:00pm Local News and Weather (extra 5mins)
That schedule is never going to happen in a month of Sundays. For starters, they're not going to start the news at 1.20 - the BBC News is still on at that point, and 1.20 is a bit of an awkward time to start the news anyway. 1.30 is much cleaner (well, strictly speaking it's 1.28, but what's a couple of minutes between friends?). I expect, if Jeremy Kyle is indeed axed permanently, they will just put another programme in its place - maybe a new programme, or quite possibly, as you suggested, Judge Rinder.