I'm looking for romance manga where the relationship already exists (or is established within a few chapters, like Horimiya if I remember correctly!

Please point me in the right direction of series or tags! Thanks 🙂 (p.s. i don't care if its yuri or yaoi or het!)

I think trying romance + slice-of-life will usually get you something along these lines. You could also try the Couple Growth tag.

14-sai no Koi
Aishiteru (Fujitani Youko)
Boku to Watashi no Henai Jijou
Bonnouji
Collectors
Dear Green
Dining Bar Akira
Fujiyama-san wa Shishunki
Haru no Houtai Shoujo
Mirai no Kioku
Otoyomegatari (kind of)
Shinkuu Yuusetsu (kind of)
Story of Someone We Know
Tsuru Tsuru to Zara Zara no Aida (at least it seems to be heading in that direction)
Yome ga Kore na Monde.

If you don't know which categories to look for, you can always try the forum search, which usually provides you with plenty of similar requests. People don't mind necro-posting here, so you can just revive an old thread if it fits your criteria.

Hetero couple:

• romance where the main couple is a couple already
• Couple from the start
• Romance where the girl and guy get together early on
• romance with couples geting together early
• Manga with early starting relationship
• A romance who shows the lead characters after they start dating
• looking for a manga about a relationship
• A couple who are together from the beginning of the manga
• Already a couple

Homo couple:

• They are lovers from the start
• already a couple from the beginning of the plot

I second Suxinn's recommendations. Also check out MITSUKI Kako's works. Her main couples tend to start dating right away.
Here are more suggestions in case your craving for those manga gets really bad:

MATSUMOTO Tomo's Kiss
A well-developed age-gap romance where the couple gets together in the first chapter.

Apart Mate by INUGAMI Sukune
Light-hearted, episodic merry-go-around about different couples' apartment life. Quirky and strangely graphic.

NANAMI Mao's 3D Kanojo
A loner otaku starts dating the school's confident beauty. The emphasis lies on the high-school couple growth.

Ojojojo by Cool Kyoushinsha
This one is a gem among the rom-com 4-koma. In spite of the female lead's tsundere tendencies and the male lead's lack of expression, they manage to get their feelings across. Not only do they compliment each other well, they also prompt each other to grow as a person and as a couple.

OOSHIRO Youkou's Sachiare!
A fluffy slice of married life about a high schooler and his older wife.

Itoshi no Kana and Ai-Ren by TANAKA Yutaka
Unusual supernatural/ Science-fiction take on the romance slice of life genre. Both couples get together early on, and they grow very close over the course of the series. The overall tone may be harmonious and very tender, but the author likes to tug on the readers' heart-strings every now and then.

AMAZUME Ryuta's Toshiue no Hito
Dramatic but satisfying romance between two post-secondary students with an age gap and some emotional baggage. Sweet and explicit.

YOSHIDA Motoi's Natsu no Zenjitsu
The author paints a painfully realistic picture of the relationship between an art student and a gallery owner. Mature storytelling, art and content.

Yonensei and its sequel Gonensei by KIO Shimoku
Another uncomfortably realistic story about a pair of post-secondary students. It's a slow rollercoaster ride, so don't expect a rose-coloured love story.

[color=#8A795D]"Stories are what death thinks he puts an end to.
He can't understand that they end in him, but they don't end with him."

• Ursula K. Le Guin, Gifts[/color]

To be savoured:

• Blood Alone by TAKANO Masayuki
• Otoyomegatari by MORI Kaoru
• Gangsta. by Kohske
• Seishun Kouryakuhon by AKIZUKI Sorata