How about

Microdisney - Town to town

The Stunning - Half Past Two

Aslan - This Is

There were a good few Irish hits during the 80s that didn't get much UK airplay

Me too ! Perhaps it's not quite as under-rated as we thought !

Others that sprang to mind are Hey Matthew, by Karel Fialka, Paranomia, by Art Of Noise feat. Max Headroom and Live It Up by Mental As Anything. No idea if they're under, over or just the right amount of rated, but they're among my favourite 'non-obvious', shall we say, 80's hits.

RAP https://www.youtube.com/watch?v=bfvJAcou96s

KIRSTY https://www.youtube.com/watch?v=7qZ2KFRaYtA

CHAMELEONS https://www.youtube.com/watch?v=4sL-wu5oa1w

https://www.youtube.com/watch?v=Zi_XLOBDo_Y

Do you like any other singers besides him then? I love traditional country but hadn't heard of him until you mentioned him.

Yello - I Love You...and The Rhythm Divine (with Shirley Bassey, plus backing vocals from Billy "Associates" McKenzie)

Less successful than their biggest hit "The Race", but I always preferred them.

martha and the muffins - was ezo ... no youtube vid
wah heat - better scream - https://www.youtube.com/watch?v=NDL010AUCt8
donald fagan - new frontier - https://www.youtube.com/watch?v=Y8zrKnkd6ss

The Lotus Eaters - 'First Picture of You' (1983)
https://youtu.be/eEE-Hl80fFk

my favourite song of all time

Yeah, beautiful song.

And another couple,
10,000 Maniacs - "My Mother The War' (1983)
https://youtu.be/OTTUKe33rFo

House of Love - 'Christine' (1988)
https://youtu.be/OXOgRvj76zI

This right here is why I say anything about him. Because sadly there are a lot who don't know of Billy Joe. To me, if you love your favorite enough, spread the word about them, especially if they are not as well known as others.

Anyways my other favorite singers, and I have several, are James Otto, Alison Krauss, LeAnn Rimes, Tanya Tucker, Trace Adkins, Darryl Worley, Brad Paisley, Toby Keith, Kenny Chesney, and Hal Ketchum.

God bless you and them and Billy Joe's family always!!!

Holly

P.S. If you love country music that is traditional sounding, Billy Joe is who you should check out. That form of music is what came from him starting in the 1980's. Before then, what was labeled rock music at the time is what the late beautiful precious was singing, so it isn't just one form of music that you get from him...or is it...considering how much has changed in music since then that is? His album named The Royal Treatment is the album from him that I listen to the most.

Paris - Another Sad Affair

https://www.youtube.com/watch?v=Ih6tnKSwgZg

An underrated classic, I reckon.

What a guitar riff!

Love and Money - Hallelujah Man

https://www.youtube.com/watch?v=V--hWckaBvg

One my all time fave songs from the 1980s.

Superb! Love that one.

Not sure if this will count but how about 'there is a light that never goes out' by The Smiths.

Sandie Shaw - Are You Ready To Be Heartbroken?

My God it's gorgeous, the original by Lloyd Cole is OK but this is on another level. Only discovered it this year and played it 40 times in a row!

http://youtu.be/HyxeyzfVGxI

How about China in your Hand by T'Pau? I know it was No 1 but seems to have been mocked relentlessly ever since.

really?....

Added some links if anyone wants to hear them

Another suggestion
Bagatelle - Summer In Dublin https://youtu.be/MMhWll_mfGk

Thanks Cork. I'll give all the linky's a listen during the week.

A lot of critics consider it overblown and pretentious.

I melt with you Modern English
Wonderful life Black

as do i, not sure how it can be underrated though.... hey ho, vive la difference!

The Monitors - Singing in the 80s
https://www.youtube.com/watch?v=UNQ9FQMNV4s

Felt - Primitive Painters

Siouxsie & The Banshees - Alot of their singles stalled around the top 30-40 mark

Marc Almond - As above, you could argue that they're not underrated, they've certainly had enough audiences to keep them going, however, they should've been selling out stadiums around the world, beyond their 'cult' fame.

Holy Ghost! Yes. defo underrated.

Roisin Murphy - RATED HIGHLY, but deserving of more than her current cult status. Too 'difficult' for le bland mainstream.

Billy Mackenzie/The Associates - see Marc Almond/Siouxsie...

You could say the same about the Clash. Only two top twenty singles in the 80s, despite being highly rated by critics and fans.

For a highly influential 80s band that completely failed to trouble the singles charts you can't get much better than Magazine:
A Song From Under The Floorboards - https://youtu.be/7ExpiNKZWKw
About The Weather - https://youtu.be/cIlrI37lo2Y