In the UK I too have found that dementia sufferers often have surprising recall of their childhood and the songs they sang and can be a springboard for reminiscence sessions about schools, toys, games, food etc. Some examples:

I've Got Sixpence
Coming Round The Mountain
Molly Malone
Quartermaster's Stores
Teddy Bears' Picnic
All Things Bright And Beautiful
Loch Lomond

As has been pointed out above, the key decades are the 1930s and 40s but I would add a cautionary note that constant references to the Second World War can sometimes cause distress to those who lived through the blitz. With that caveat in mind some of the songs of the time can be very evocative, eg:

Wish Me luck As You Wave Me Goodbye
White Cliffs Of Dover
Bless 'Em All
Lilli Marlene
A Nightingale Sang In Berkeley Square
...and anything by Flanagan & Allen and George Formby.

Others which always seem to work:

When I Grow Too Old To Dream
Old Man River
Side By Side
You Are My Sunshine
Deep In The Heart Of Texas
Apple Blossom Time
Don't Fence Me In

Of course any list of songs would have to include a selection of those loosely categorised as Music Hall or Cockney and which are embedded in the national psyche. Obvious examples:

Daisy Daisy
Show Me The Way To Go Home
I Belong To Glasgow
Roll out The Barrel
If You Were The Only Girl In The World

Most of my work these days is in this sector so if anyone would like a fuller list of recommendations please PM me.