Ant and Dec weren't on in May, but were earlier in the year IIRC. Richard and Denise did all the Bigger Breakfasts in May, July and August 1997, bar those news specials for Diana's death. I think she died in the middle of (what was meant to be) a 2 week stand-in run for Jayne Middlemiss. She didn't appear the Monday after Diana's death nor the Friday. (I think Richard presented with, randomly, Joely Richardson on the Friday?)
I was getting a bit confused there, I had more or less given up on it by that point. As I remember, on the Monday after Diana's death, it was Richard Orford and Vanessa Feltz in The Mall, reading out faxes, reviewing the papers and introducing extended news bulletins, and it ended at 9am and C4 continuity took over for the rest of the morning.
I think on the Tuesday Vanessa presented again until 9am at which point Jayne Middlemiss took over for The Bigger Breakfast, then on Wednesday and Thursday it was more or less business as usual. On the Friday, though, because the funeral was the next day it was another news special. This was an OB, I don't think they ever said where from, with Richard Orford and, as you say, Joely Richardson plus also a returning Peter Smith as an interviewer, I remember Bob Geldof among the guests. Think that might have finished at 9am as well. Then Johnny Vaughan started the following Monday, as planned.
Though a little awkward, they certainly managed better than they would often do when a big story was breaking. The one I always remember is the day after Dunblane which was just a really awkward compromise because you had extended news bulletins but a lot of the regular features, so there were loads of very jarring changes of mood, it just seemed a bit tasteless, which is a problem you were always going to have with a show like The Big Breakfast but especially so with inexperienced presenters and producers. There was also a huge cock-up that day because C4 had an ident with Mark Little firing a gun at the camera, and they forgot to take it off the system and played it at 7am, and they had to do an apology.