You can get natural fibres for cheap, you just have to look in the sales and online.
I wouldn't really recommend high street stores currently - Next, M&S, H&M etc are all becoming more and more synthetic, although they do have an occasional good buy it's harder to find.
I tend to look at places like white stuff, seasalt, crew clothing, brakeburn, BAM, rapanui, passenger. I usually buy these brands in the sales and on Vinted, because they are expensive otherwise, but I'd rather that than the cheap synthetics on the high street.
I got a really nice pure merino wool jumper from Crew in the sale for £18 the other day (down from £70). That's unusual but it's doable.
Also, don't buy things too often/ for the sake of it - just keep an eye out and get better quality things as and when you see them on sale.