Is it that companies have front end/full stack roles that they only want filled by either experienced devs from other companies, or current employees (who entered either from other companies or their grad program)?
from what I've seen, when a company starts hiring, the first thing they'll do is see if someone knows someone for the job and if not they will either offer the roles to people inside the company first (and people can refer their friends into the roles). after that, the roles either end up on the internet or they hire a contractor or consultant to fill it.
for example, a company might have a ratio of 50% permanent staff to 50% consultants/contractors (probably the reason why consulting companies seem to take in more grads than the others...).
for a lot of the companies like the banks, colesworth, etc the majority of the entry is through the internships and graduate programs. if possible I would pick a university with a guaranteed industry placement, although of course there aren't guarantees there you can end up in non coding roles, internships imo try and get any software engineering internship possible and aim to get a return offer. graduate progrms try and get into software engineering programs over technology graduate programs and if you end up in technology try and find out what the software engineering teams are looking for if you want to go there.
you might find out what % of grads get into software engineering rotations etc by looking at the profiles of graduates on linkedin and asking them about it.
in terms of actual jobs you can also apply to these but I got bounced back a lot and redirected to grad roles even with experience.
some of the people I know succeeded in getting out of roles which were nothing to do with dev work after a year by applying to other companies. in fact like 7 people I know left before the year was up because they did not get what they wanted to do.
I've also talked to people who were unable to move into what they wanted because they stayed too long in a certain role.