There are sooo many nice bras you can get in that size. You have a bit more choice than me, as not all brands do 28 bands! I wear your sister size, 28G, and I have far more bras than I need tbh, haha. Some brands you could look at are Masquerade (one of my favourites), Freya, Cleo, Curvy Kate, Wonderbra, Boux Avenue, Parfait By Affinitas, Lepel...there are plenty. Cheap places to buy bras are BraStop, MyCurvesAndMe, Amazon, ASOS (pretty sure their own-brand bras and bikinis sometimes go to a 30FF), eBay (if you need a sports bra you can usually find Shock Absorbers for under £15), Debenhams, Figleaves...and there are loads more.
Losing weight may help, but it's not guaranteed - you might just find yourself in an even more awkward-to-buy size - I actually just went from a 30F to a 28FF and now 28G when I lost a bit of weight, which means my boobs pretty much stayed the same size and I just lost a bit of fat from my ribcage.
It's silly to talk about a body part you have very little choice over being 'in fashion'.