Personally, I keep everything simple and straight to the point:
I introduce myself, showing them the revenue I generate by selling other brands, who I am, and what I can do for them.
I explain the reasons why their brand is not performing well on Amazon (bad listings, poor photos, inadequate bullet points, etc.) and promise them that I will work on the listings to make them look great and invest in advertising out of my own pocket.
In short, make them trust you and make them aware of the benefits of working with you.
This approach is just me; I keep everything straightforward. I don’t like kissing asses just to get permission to sell their brand.
Seems like they are already in the market. They are currently not selling but keep coming on and off on amazon Uk. Which affects their ranking.
But when they sell it sells good and quick. Just need some marketing in UK.
I did OA on their listing and made good profits but now they don’t allow bulk buying on their website. And they don’t have distributions in UK.
So as they are not that big brand i think its good space to contact and spend some good money with them on their listing and ranking. And make a permanent top ranked brand on Amazon uk.