No, is the short answer. As above you can do a bioscience degree which is probably the more relevant/direct route. There are various options in this regard depending on exactly what your interest is (e.g. microbiology, biochemistry, biomedical sciences, pharmacology, physiology, infection and immunity/immunology, etc, etc). As above a PhD would be essential and a masters may also be necessary (either an undergraduate integrated MSci or a BSc/BA + MSc or similar).
If you're specifically interested in immunology you may find various courses in infection and immunity or immunology (UCL has a course in infection and immunity, Bristol has courses in immunology which may be combined with e.g. virology, and Manchester has a course in virology) since it is so specifically relevant to your interests. However a degree in any bioscience subject broadly with a more specialised masters would be just as good too.
That said "immunologist" is a term for a medical doctor specialising in the immune system and related diseases, which may be the source of the confusion. They aren't research scientists (necessarily) but are clinicians in that area directly treating patients and arranging treatment plans etc. That would require a medical degree. Some immunologists may also go into immunology research though and get a PhD etc as above.