1.SILVER SPOON IN MY MOUTH-Raymond M https://youtu.be/6ILzvnaSo-Q
2.I'VE HAD ENOUGH https://youtu.be/aUYVnj0qZA0

Thanks for showing us your favorite music with those videos.  I'm sorry, but based upon that.  I'm not sure what I might recommend.  
Possibly a good psychiatrist. 

No Really,  I'd be interested in a current artist that recorded with a Lennon/McCartney flavor
Walter from the other side?

Paul Myers and John Moremen - The Paul And John
Smith And Hayes
- Jordan/Wilson. Listen to their Flamin' Groovies Shake Some Action album for the best example. Produced by the great Dave Edmunds.

- Marshall Crenshaw. And not just because he played Lennon in the stage production of Beatlemania. A great, great songwriter, excellent musician, passable singer (contrary to Jagger's assertion, it's the song, not the singer ;-) .

- Dwight Twilley. He shoulda had Tom Petty's career. Better songwriter, better singer, had a better guitarist than Mike Campbell in Bill Pitcock IV, and a great drummer/harmony singer/partner in Phil Seymour. Bill and Phil are both dead, leaving Dwight alone in Tulsa, putting out the occasional album. It's a cryin' shame.

- All the guys in the "classic" NRBQ line-up (Terry Adams, Joey Spampinato, Al Anderson). Along with The Band, amongst the greatest self-contained ensembles (writing, singing, playing) in all of Rock 'n' Roll history. IMO, of course. Al left the band to concentrate on songwriting, and relocated to Nashville, home of great songwriting.
bdp24 above has some great recommendations,

I would add to his list:

-Brian Wilson
-10cc (Godley-Creme and Stewart/Gouldman)
-Electric Light Orchestra (Jeff Lynne)
-Harry Nilsson 
-Todd Rundgren 
-Eric Woolfson - Alan Parsons Project 

I may have taken the OP’s post too literally in that... (two) songwriters that worked together.