Why does Margaret Thatcher's narration come in the middle while Dennis is speaking to her?

She appears to be trying to distract herself from the vision of her dead husband as well as attempting to recall June's name.

I haven't seen the film, but from the script it sounds like she's trying to ignore the vision of her husband and attempt to recall June's name.

She can't remember the name initially, but is able to recall a complex Rudyard Kipling quote until she eventually remembers the name.

INT. DRAWING ROOM. CHESTER SQUARE. PRESENT. DUSK.

MARGARET sits reading DENIS’ spy novel.

DENIS: She does it in the end. Kills him

MARGARET slams the book closed.

DENIS (CONT’D): I don’t know why you’re being so scratchy.

MARGARET’s eyes dart to the clock.

DENIS (CONT’D): It’s not as if you’ve got anyone else to talk to.

Shaking her head, MARGARET tries to block him out.

MARGARET (V.O.): When the Himalayan peasant meets the he-bear in his pride -

DENIS: You know, it’s a marvel to me that you can still quote huge chunks of Kipling but try remembering the name of that woman who’s just made you that godawful cold collation... No? Come on... you can do it... month of the year... one syllable... rhymes with moon ...

MARGARET: (sudden/like a lightbulb): June.

MARGARET turns to DENIS, a quiet appalling victory.

DENIS: June! Bingo. Knew you’d get there in the end. “When the Himalayan peasant meets the he-bear in his pride, He shouts to scare the monster, who will often turn aside, but the she-bear thus accosted rends the peasant tooth and nail. For the female of the species is more deadly than the male...”

As he continues, MARGARET reaches for the remote, turns the television on. She moves onto the radio. Then the stereo. She moves on, talking to herself -

In her final years, Thatcher developed dementia. Many people with Dementia are unable to retain short-term memories but can recall details from many years before.

The scene seems to be a way to show how her mind and memory were working at that time of her life.