I have a few brands to suggest!
For shoes:
Wills Vegan shoes, very comfortable and well made. Tend to be more on the simple/classic side - I have brogues and worker boots from this brand. My boots are maybe 5 years old and still look good as new. They also sell some bags (satchels and classic styles) and belts.
Beyond Skin. More fashionable/interesting styles. Although I’ve found the quality not as good as you’d expect for the price - I’d only recommend getting something on sale. They do have good sales though.
I also like Bhava, I have one pair of boots from them. They don’t have loads of styles but some simple classics.
For bags my favourite brand is Angela Roi. You can get them in the UK from Naturismo although they don’t do the full range.
I also really like Wilby Clutch (cork bags in bright colours) and La Bante. Both are good quality and last well.
Also some non-vegan brands have vegan options, I have a vegan pair of DMs and a vegan pair of Vejas.
Actually, a good place to start is Immaculate Vegan which is a marketplace so would give you a good intro to lots of different brands.