The answer is to use a template file, but it needs a bit of tweaking for the logo bit:
---
title: "My report"
author: "me"
output:
pdf_document:
toc: yes
includes:
in_header: style.tex
---
Prepare the document "style.tex" in the same folder as your markdown file and make sure you have changed you working directory in R to this folder.
Add the following lines to your "style.tex" file:
\institute{My institute}
\pgfdeclareimage[width=2cm]{logo}{logo.png}
\usebackgroundtemplate{\pgfuseimage{logo}}
Thanks to:
Inserting logo into beamer presentation using R Markdown