No worries, glad to be of assistance. So grad schemes wise, I'll give you some public and third sector ones as that's what I am most familiar with, I am sure if you ask your uni careers service or look on thestudentroom forum there are lots of others too. Graduate schemes are great as a managed introduction to work with lots of support, training and the chance to be part of a 'cohort', plus you get to do various different roles within an organisation so a excellent opportunity to find the kind of role you eventually want to do permanently. Of course they do tend to be competitive entry, some of the largest e.g. NHS and Civil Service are hugely oversubscribed. But it isn't all about exam results and who went to the best university, the schemes place a lot of emphasis on potential and leadership/people skills plus good experience and the ability to articulate yourself well so if you have those things you'd stand an excellent chance!
And even if you don't want to go down the grad scheme route, take a look at some of the info on the scheme pages about the types of job the trainees could be doing and see if something takes your fancy, these types of role can be available as direct entry too...
so some links...
The NHS has an excellent albeit highly competitive graduate scheme with various strands including HR:
www.nhsgraduates.co.uk/
The civil service fast stream is highly prestigious and so again competitive, there is the general fast stream and then separate streams for HR, Comms and others
www.faststream.gov.uk/
As you are interested in teaching you might want to look at Teachfirst, I think quite a lot of people do the programme and don't end up teaching or in traditional teaching roles anyway, as the programme gives you a depth of experience
www.teachfirst.org.uk/
CityYear and IntoUniversity are other placement schemes in the education/teaching area: intouniversity.org/graduatescheme
www.cityyear.org.uk/
Local government have a graduate development programme, more tailored towards general and financial management but could be an interesting way in:
www.local.gov.uk/national-graduate-development-programme/about-ngdp
Cancer Research UK is probably the best known/well established grad scheme in the third sector, has various streams including HR and Comms: www.cancerresearchuk.org/about-us/graduates-and-interns/our-streams
Wellcome Trust are also a huge charity and they run a scheme including Comms: wellcome.ac.uk/jobs/graduate-development-programme
I'm not very familiar with this one but CharityWorks have an interesting looking programme which features Comms quite heavily: www.charity-works.co.uk/graduate-programme/
Hope some of these are of interest!