"Every visit for the last seven years, she hasn't recognised any of us. But when we have a good visit - and they're not always good - when we leave, she won't remember that we've been there but the sensation of being in the company of someone who loves you is something we can't deny.
"There's a calmness, there's a companionship: these really fundamental feelings of being loved, being taken care of by people and family who really love you, I think that's something that regardless of how progressed your dementia is stays with you. That's a real argument for people going to visit loved ones regardless of how far progressed their disease is."
The Academy Award-nominated actress, who is married to Mumford & Sons frontman Marcus Mumford, made the personal admissions as part of a campaign to change public perception of the disease.
She told radio hosts Nick Robinson and Justin Webb that she felt 'lucky' to be able to speak out for charities, although she favoured keeping her personal life private.
Miss Mulligan has previously told how her grandmother's illness has progressed from forgetfulness 15 years ago to living in a care home. But though there were "terrible visits where we've all ended up in tears", she said there were also visits "where something really magical happens".
Sir Michael Parkinson, whose mother suffered from dementia, and Michael Palin, whose Monty Python co-star Terry Jones has the disease, joined her on the programme.
Parkinson echoed her sentiments, adding "There is a tendency for some people to say if he or she doesn't recognise me... as far as I'm concerned they're dead. It does happen.
"You have to hope that if it happens to you, you don't feel that kind of rejection."
Palin said: "I do think it's terribly important to continue to relate to that person, to make sure they're not considered to be in a different group from the rest of humanity."