Inclusion Criteria:  Written (signed and dated) informed consent and be capable of co-operating with HMBD-001 administration and follow-up.  Histologically confirmed advanced or metastatic solid tumours resistant or refractory to conventional treatment, or for which no conventional therapy exists or is not considered appropriate by the Investigator or is declined by the patient.  Part A Arm 1 Monotherapy Dose Escalation:  Patients with tumour types known to overexpress HER3 including:  Bladder cancer Triple negative breast cancer Castration resistant prostate cancer Cervical cancer RAS wild type colorectal cancer Endometrial cancer Gastric cancer Hepatocellular carcinoma (HCC) Melanoma Non-small cell lung cancer (NSCLC) Oesophageal cancer Ovarian Cancer Pancreatic cancer Squamous cell cancers of the head and neck  Part B Arm 1 Monotherapy Dose Expansion:  Patients with castration resistant prostate cancer, RAS wild type colorectal cancer, triple negative breast cancer or squamous cell cancers of the head and neck with confirmed high HER3 expression by Immunohistochemistry (IHC) on pre screening biopsy prior to study enrolment or confirmed existing NRG1 gene fusion.  Life expectancy of at least 12 weeks. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. Haematological and biochemical indices within the protocol specified ranges. Patients with advanced prostate cancer must have castrate levels of testosterone and have received a next generation hormonal agent (at least one of abiraterone, enzalutamide, apalutamide or darolutamide). Aged 16 years or over at the time consent is given.  Exclusion Criteria:  Radiotherapy (except for palliative reasons), chemotherapy, endocrine therapy (with the exception of life-long hormone suppression such as luteinising hormone-releasing hormone (LHRH) agents in prostate cancer), immunotherapy or investigational medicinal products during the previous 4 weeks before trial Cycle 1 Day 1. Patients with ongoing toxic manifestations of previous treatments greater than NCI CTCAE Grade 1. Exceptions apply. Patients with symptomatic brain or leptomeningeal metastases should be excluded. Exceptions apply. Women of child-bearing potential (or are already pregnant or lactating). Exceptions apply. Male patients with partners of child-bearing potential. Exceptions apply. Major surgery from which the patient has not yet recovered. At high medical risk because of non-malignant systemic disease including active uncontrolled infection. Known to be serologically positive for hepatitis B, hepatitis C or human immunodeficiency virus (HIV) infection. Known or suspected hypersensitivity reaction to previous biological therapy that in the opinion of the Investigator is a contraindication for their participation in this study. Concurrent congestive heart failure, prior history of > class II cardiac disease (New York Heart Association [NYHA]), history of clinically significant cardiac ischaemia or prior history of clinically significant cardiac arrhythmia. Patients with significant cardiovascular disease as defined in the protocol are excluded. Patients with an active autoimmune disease including but not limited to myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjögren's syndrome, Guillain-Barré syndrome, multiple sclerosis, vasculitis or glomerulonephritis. Exceptions apply. Patients receiving doses of prednisolone >10mg daily (or equipotent doses of other corticosteroids) within 7 days prior to the first dose of study drug are not eligible unless administered as pre-medication. Patients having received a live vaccination within 4 weeks prior to first dose of HMBD 001. Is a participant or plans to participate in another interventional clinical trial, whilst taking part in this Phase I/IIa trial of HMBD-001. Participation in an observational trial or interventional clinical trial which does not involve administration of an IMP and which would not place an unacceptable burden on the patient in the opinion of the Investigator and Medical Advisor would be acceptable. Any other condition which in the Investigator's opinion would not make the patient a good candidate for the clinical trial. Current or prior malignancy which could affect safety or efficacy assessment of the IMP or compliance with the protocol or interpretation of results. Patients with curatively-treated non-melanoma skin cancer, non-muscle-invasive bladder cancer, or carcinomas-in-situ are generally eligible.