Combination Study of Guadecitabine/ASTX727 and Pembrolizumab

Inclusion Criteria: 1. Part A and B1/2: Histologically or cytologically confirmed advanced solid tumours, refractory to conventional treatment, or for which no conventional therapy exists or is declined by the patient. Part B1: Histologically or cytologically confirmed advanced solid tumours, refractory to conventional treatment, or for which no conventional therapy exists or is declined by the patient AND: * Patients with any tumour type that previously responded to a PD-1 or PD-L1 inhibitor and subsequently progressed (defined as secondary resistance to PD-1/PD-L1 inhibitors ie CR or PR by RECIST, or SD by RECIST for 6 months' duration) or/ * Patients with microsatellite-instability-high (MSI-High) tumours, provided they have been defined by validated assays or patients with deficient mismatch repair (dMMR) defined by immunohistochemistry, who have previously received and have progressed on a PD-1 or PD-L1 inhibitor (primary resistance to PD-1/PD-L1 inhibitors) or/ * Patients with other solid tumour types who could benefit, based on emerging anti-tumour activity data, from combination therapy with a demethylating agent and PD-1 or PD-L1 inhibitors, in consultation with any other relevant preclinical or clinical data, at the Chief Investigator's discretion. Part B2: Patients with histologically or cytologically confirmed NSCLC previously treated with PD-1 or PD-L1 inhibitor for advanced or metastatic disease. 2. Life expectancy of at least 12 weeks. 3. Eastern Co-operative Oncology Group (ECOG) performance status of 0-1 with no significant deterioration over the previous 2 weeks (Appendix 1). 4. Evaluable or measurable disease as assessed by RECIST 1.1. 5. Haematological and biochemical indices within the ranges shown below. These measurements must be performed within one week (Day -7 to Day 1) prior to administration of any investigational medicinal product. * Haemoglobin (Hb) ≥ 9.0 g/dL * Absolute neutrophil count ≥ 1.5 x 109/L * Platelet count ≥ 100 x 109/L * International normalised ratio (INR) ≤ 1.5x upper limit of normal (ULN) Or: Prothrombin time ≤ 1.5x upper limit of normal (ULN) * Serum bilirubin ≤1.5x ULN Or: Direct bilirubin (for patients with total bilirubin \>1.5x ULN) ≤ 1.5x ULN * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5x ULN (for patients with liver metastases ≤ 5x ULN is permissible) * Calculated creatinine clearance (per institutional standard) ≥ 50 mL/min 6.18 years or over. 7. Written (signed and dated) informed consent and be capable of co-operating with treatment and follow-up. 8\. Agree to the use of archival paraffin embedded tissue (if available) for PD-L1 (programmed death-ligand 1) analysis 9. Agree to provide a fresh tumour biopsy at baseline and on Cycle 2 Day 8 of a tumour lesion not previously irradiated (tumours progressing in a prior site of radiation are allowed for PD-L1 characterization, other exceptions may be considered after consultation with the Chief Investigator). 10\. Female subjects of childbearing potential should have a negative urine or serum pregnancy test within 14 days prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. 11\. Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 6 months after the last dose of study medication. Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \>1 year. Decitabine, a metabolite of Guadecitabine/ASTX727, can affect fertility and so oocyte cryopreservation should be discussed with female patients. 12\. Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 6 months after the last dose of study therapy. Decitabine, a metabolite of Guadecitabine/ASTX727, can affect fertility and so cryopreservation of sperm should be discussed with male patients. Exclusion Criteria: 1. Radiotherapy (except brief course for palliative reasons), endocrine therapy, immunotherapy or chemotherapy during the previous four weeks (six weeks for nitrosoureas, Mitomycin-C and 4 weeks for investigational medicinal products) before treatment, except for hormonal therapy with luteinizing hormone-releasing hormone (LHRH) analogues for medical castration in patients with CRPC, which are permitted. 2. Patient has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ bladder or cervical cancer that has undergone potentially curative therapy. 3. Spinal cord compression or brain metastases unless asymptomatic, treated and stable and not requiring steroids for at least 4 weeks prior to start of study treatment. 4. Ongoing toxic manifestations of previous treatments. Exceptions to this are: * Grade 1 toxicities, which in the opinion of the investigator should not exclude the patient * Alopecia of any grade 5. Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 14 days prior to the first dose of trial treatment. The use of physiologic doses of corticosteroids may be approved after consultation with the chief Investigator. 6. Has an active autoimmune disease that has required systemic treatment in past 3 months (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. Patients with Sjogren's syndrome will not be excluded from the study. In addition patients that experienced a Grade 2 or higher immune-related AE's on treatment with immunotherapy will be excluded from the study. 7. Has evidence of interstitial lung disease. 8. Has a history of (non-infectious) pneumonitis that required steroid treatment or has active pneumonitis. Pneumonitis includes acute interstitial pneumonitis, pneumonitis and idiopathic pneumonia syndrome. 9. Active infection, requiring systemic therapy. 10. Has received a live vaccine within 30 days of planned start of study therapy. Note: The killed virus vaccines used for seasonal influenza vaccines for injection are allowed; however intranasal influenza vaccines (e.g. FluMist®) are live attenuated vaccines and are not allowed. 11. Major surgery (excluding minor procedures, e.g. placement of vascular access) from which the patient has not yet recovered. 12. At high medical risk because of severe or uncontrolled non-malignant systemic disease including active uncontrolled infection, active bleeding diathesis. 13. Known to be serologically positive for hepatitis B, hepatitis C or human immunodeficiency virus (HIV). Screening for chronic conditions is not required. 14. Any of the following cardiac criteria: * Mean resting corrected QT interval (QTc) \> 470 msec obtained from 3 consecutive electrocardiograms (ECGs) within 5 minutes of each other. * Any clinically significant abnormalities in rhythm, conduction or morphology of resting ECG, e.g. complete left bundle branch block, third degree heart block. * Any factors that increase the risk of QTc prolongation or risk of arrhythmic events, such as heart failure, hypokalaemia, congenital long QT syndrome, family history of long QT syndrome or unexplained sudden death under 40 years of age or any concomitant medication known to prolong the QT interval * Experience of any of the following procedures or conditions in the preceding 6 months: coronary artery bypass graft, angioplasty, vascular stent, myocardial infarction, angina pectoris, congestive heart failure New York Heart Association \[NYHA Grade 2 (refer to Appendix 4)\] * Uncontrolled hypertension - Systolic BP \>160mmHg and/or diastolic BP \>100mmHg * Left ventricular ejection fraction (LVEF) below institutional lower limit of normal. 15. History of hypersensitivity to active or inactive excipients of guadecitabine or pembrolizumab or drugs with a similar chemical structure or class to either agent. 16. Is a participant or plans to participate in another interventional clinical trial, whilst taking part in this Phase I study of guadecitabine and pembrolizumab. Participation in an observational trial would be acceptable. 17. Any other condition which in the Investigator's opinion would not make the patient a good candidate for the clinical trial.