You can't 'continue' with only research at Postgrad unless you do an MRes. Very few Depts would let you progress straight to a PhD in Psychology without a Masters - either by research or taught.
You won't be encouraged to just make your undergrad diss. 'bigger' or to take up a Masters place praparing a manuscript of an existing project 'for publication' - you do that in your own time. The whole point of doing research at postgrad is to work at great depth on something smaller or different, so as above, you need to pull something out of this existing work and make a realistic (but different) research proposal out of it. If you have ambitions of a PhD and an academic career you need to have several research interests not just one, so you need to widen your general areas of study - which is why most people who do progress to postgrad start with a taught Masters degree.
Be aware that postgrad funding is not a right or automatic. There is no SF at postgrad level and Masters funding outside obvious STEM subjects is almost non-existent - can you afford £25k a year out of your own pocket? There is precious little funding around at PhD level even - and what there is will be usually formulated around a specific project/research group - ie. not necessarily what you are interested in.
Btw, no serious academic publisher would publish something by a graduate straight out of a first degree. The best way to start would be to write up the crux of your argument/findings as a short journal article (ask your ex-tutors for advice on a relevant journal) or to present it as a paper at a Conference. This is how you build your credibility - and make getting Masters and/or PhD funding more likely.