Primary Education degrees normally allow you to gain QTS. I did this in my first year but had to changed to a non QTS degree so that I can gain some experience at a school in an environment when I'm not being assessed I struggled with my first placement, so transferred to a non QTS degree and did some voluntary work at a school alongside it I'm now going to apply for a PGCE in 2021.If you want to be placed in a school straight away and become a teacher as soon as possible, then do a QTS degree. If you do a non QTS degree, you can then work in a school and build some experience so you can then do a PGCE. This will take a year longer, however.
The university you do it at doesn't really matter as schools tend to just want QTS. If it helps I got onto a primary education degree at Hertfordshire when my A-Levels were BCE.