Spirit,
Like Bunny, I am also not in UK, so don't know about NHS
standards.
Sometimes dream interpretation is used as part of psychodynamic therapy, so perhaps this is what is meant by side treatments with added pay. Though a main psychoanalytic therapist could do it (and just about everything I'd guess), without sending you elsewhere/specialist.
Maybe you are seeing a couselor mainly, with some sporadic input from a therapist, that would require the added $. I don't know if it differs in the UK in that credentials for a counselor (and what they are able to do) would differ from a therapist. I really couldn't say without more info.
You can always search online for NHS standards, and hook up with some discussion groups related to therapy, that are UK based. This might help answer some of your questions better.
As far as the therapy, though there are similarities, there are differences between psychodynamic therapy and psychoanalysis.
Again, I'd recommend doing an Internet search on PD therapy, and you will find out much, much more than someone could write here in an answer for you.
There is a ton of very, very detailed information regarding all therapy types, and why they are suggested.
Also, do not hesitate to ask your actual therapist or counselor about these things. They should be willing to take the time to explain to you why they suggested this for you, and the goals of treatment.
If you ask, you will get an answer most specific to you (as opposed to general aimed online reading), meaning, what about your specific circumstances would make x therapy type a good choice.
Best of luck!