I have a name which is easily misspelled and have frequently been ticketed with spelling mistakes. The general rule of thumb that I have been told is that two spelling mistakes is fine, and I would have thought that since Debbie is a very common version of Deborah then she has a good chance.
The main problem I see is that it's hard to know whether you'll be OK until you actually fly. You you try calling BA at LHR since it's their decision. She should be able to fly from Shannon to LHR without a passport anyway.
Does she have any other Photo ID with Debbie on it? Can't hurt to have as much as possible with her.