After his seminal 1972 discovery of the role of complement in the induction of antibody production and related work, Pepys has mostly worked on amyloid and acute phase proteins. He has illuminated the pathogenesis and natural history of systemic amyloidosis, transforming diagnosis of this fatal disease, and improving management and survival. He has also elucidated the structural properties, function and clinical significance of serum amyloid P component (SAP) and C-reactive protein (CRP). He first identified these proteins as therapeutic targets, and has designed and is developing new drugs aimed at them.

His invention of in vivo scintigraphy with radiolabelled SAP enabled systemic amyloidosis for the first time to be safely, non-invasively diagnosed and quantitatively monitored. This revolutionised understanding of the natural history of amyloidosis and its response to therapy, and has guided radical therapeutic developments, focusing attention on the crucial importance of reducing the abundance of amyloid fibril precursor proteins. Pepys has discovered many of the mutations responsible for hereditary amyloidosis, including the first human lysozyme mutation, leading to demonstration that amyloidogenic lysozyme variants are less stable than wild type lysozyme and construction of a widely accepted general model of amyloid fibrillogenesis.

Pepys first suggested a small molecule therapy for amyloidosis in 1984. His novel SAP targeting drug, CPHPC, hexanoyl bis(D-proline) (Nature 2002), was an American Chemical Society medicinal chemistry highlight of 2002. CPHPC depletes circulating SAP almost completely, reduces the SAP content of systemic amyloid deposits and completely removes SAP from the brain. Use of the drug for SAP depletion in Alzheimer's disease is being tested in the NIHR funded DESPIAD phase 2b clinical trial.

Pepys also invented the obligate partnership of CPHPC with anti-SAP antibody for treatment of systemic amyloidosis, which was licensed to GlaxoSmithKline. It produces unprecedented clinically beneficial clearance of visceral amyloid deposits (New England Journal of Medicine 2015; Science Translational Medicine 2018). The WHO International Non-proprietary Names, miridesap (CPHPC) and dezamizumab (humanised monoclonal anti-SAP antibody), were assigned in 2017. However, GSK’s phase 2 study was halted in 2018 and further development terminated because of an unfavourable risk/benefit relationship in cardiac amyloidosis. Nevertheless, the efficacy of antibodies in removing human amyloid deposits is a crucial proof of concept that strongly underpins Pepys's ongoing design of novel immunotherapeutic approaches. The novel small molecules of Pepys and his team, targeting the amyloidogenic plasma protein, transthyretin, to prevent it forming amyloid, are in development supported by the UCL Technology Fund.

Pepys’s demonstration that CRP increases ischaemic myocardial and cerebral damage in vivo was the first validation of CRP as a potential therapeutic target. He rationally designed bis-phosphocholine-hexane as the first specific inhibitor of CRP (Nature 2006) and his team's development of more medicinal CRP inhibitors is now supported by Apollo Therapeutics.  Pepys identified innate host defence against pneumococcal infection as the first definite in vivo function of autologous CRP. He has also shown that human CRP is not pro-inflammatory or pathogenic in healthy individuals. He previously played a leading role in establishing the routine use of CRP testing in clinical practice. He produced the World Health Organization’s International Immunoassay Reference Standard for CRP, and also those for serum amyloid A protein, and thyroxine binding globulin.