Some brands below that have warm sounding models (ps not all models within a brand are).
amp - sugden, pass labs, luxman, gryphon (perhaps more dark than warm).
speakers - wharfedale (older models, haven’t heard the current models), epos (older models, haven’t heard newer models), many BBC based designs (Harbeth, Rogers, Spendor), Tannoy.
you don’t have to get both items with a warm tone as neutral + warm = warm.
a good example of this is the above mentioned combination of Wharfedale Linton (warm) + Audiolab 6000A (neutral with good bass weight).
also suggest that even if you can’t buy both together, you audition both and determine your selection upfront for both.
of the 2 items you have, the change in amp will give a bigger improvement (as others have suggested) ie your speakers are better than your amp in showing the improvement of the change.
hope this helps