Looking for a warm sweet speaker

The Swiss brand Boenicke are a speaker worth checking out if they are available in your area. They have this unique balance of naturalness and warmth whilst losing nothing in detail. Extraordinary speakers. The Boenicke/CAD room in Munich was one of the best sounding to my ears.

What I have heard of some Proac speakers also seem to fit your criteria. The models with the ribbon tweeter sound gorgeous.

Of the US brands I have heard the Avalon Ideal might work, it sounded terrific when I demoed it, and I felt had a more British sound for an American speaker. In Munich the Joseph speakers sounded very good too and seem to have a sound along the lines you describe, though the source in that room was a lovely reel to reel which would have helped. 

Without any possible doubt in your budget: XTZ Divine Alpha
Not sure if you can get them in the US... check it out.
Or the Tannoy Legacy Arden

Modern KEF speakers are NOT warm and sweet. If anything they are lean and somewhat bright by the OP's definition.

Don't laugh - I suggest - Magnepan .7. They are warm and sweet in the right setting :) To my ears much more laid back than the older models.

Vandersteen speakers comply with the definition, at least at the lower end of the range - 2CE, 3's.

I love my Proac D15s and also loved Vandersteens when I had them. I share your taste for the British sound. I currently have Audio Physic Avantera with BAT tube mono blocks. Resolving, layered, but still plummy sound to my ears, in my room. 

Scan the usual sale sites.  Used higher end Thiels would meet your needs, I'm sure.  I'm still running almost 30 year old CS3s anchoring my home theater.  They are full bodied yet accurate and not at all etched in the HF.