I find this thread interesting! Short answer: no you can't. Long answer....
So, I have an undergrad psychology degree (4 years, as typical for Scottish degrees). On completion I obtained a BSc (Hons) Psychology. Of course this is a taught degree and did not convey me any rights to work as a psychologist as further training is needed. I then trained in a shortened programme for undergrads in mental health nursing (28 months), which on completion gave me a BN in Mental Health Nursing and allowed me to register with the NMC as a regulated and registered professional and this, in turn allowed me to work as a Mental health Nurse. I did this for just over 4 years before applying to the DClinPsy, I was accepted and I am now in my first year of training, employed as a Trainee clinical psychologist, paid by the NHS/Health Education England and also enrolled as a full time post grad research student.
You are right that the Professions of psychology and nursing are definitely related and the two professions often work together in the same teams and with the same populations but, the scope of practice/skills/knowledge/interventions vary with some elements overlapping significantly whilst others being outwith the scope of practice of the other. Being a mental health nurse did not automatically allow me to work as a psychologist because it has its own set of competencies and requirements for training and registration via the HCPC, although I worked with a psychological eye and could complete further training to deliver some of the same interventions as psychologists. As others have stated, to work as any type of nurse you must be registered as a nurse with the NMC register for that type of nursing, a prerequisite of that is holding the relavant and appropriate training and education and holding yourself accountable to the Codes of practice and ethics.
So what am I saying? Well at the moment I am an NMC registered MH nurse who is now employed as a Trainee Clinical Psychologist. Therefore, I can currently work as a MH nurse OR a Trainee Clinical Psychologist. I cannot work as a Clinical Psychologist because I do not have the qualifications, meet the prerequisites for registration or indeed have the required HCPC registration to do so. It is also important to note that I cannot work as a General Nurse or a Learning Disabilities Nurse and so on, as I do not meet the requirements to register in those roles. If I wanted to work in another branch of nursing I would have to go back to Uni, do further study and then apply for registration separately for each branch of nursing - ie become dual-trained.
In January I need to renew my nursing NMC registration (pay £120 to the NMC) to continue to be registered. If I don't do this then I can no longer work as a MH nurse despite meeting all the prerequisites of registration.
In 2 years my NMC registration is due for revalidation (done every 3 years, alongside paying the yearly renewal fee I must submit evidence that I meet the minimum requirements to remain on the register, such as, practice hours, additional training etc). If I do not do this - I would no longer be able to work as a MH nurse as I would no longer be registered, despite having all the prerequisite registration requirements.
In 3 years I will (hopefully) have finished my DClinPsy which would confer me the prerequities for registration BUT, I would still need to apply to register with the HCPC in order to practice legally and call myself a Clinical Psychologist/get any jobs. If I have also maintained my nursing registration (I.e pay the yearly fee, meet the minimum requirements for revalidation and actually revalidate with the NMC) I could also choose to work as a Mental health Nurse at that stage too. But, crucially, neither of these registrations will allow me to work within the other profession or even sub-types of the same professions without meeting the academic and practice prerequisites for registration and actually holding that registration with both the NMC and/or the HCPC for the specific fields of practice!
I hope this helps to tease apart some of what you are talking about.