Change table numbering style to use roman numerals

Question

I am interested in using Roman numerals for the table numbers in a report I am creating, however have run into an issue as I am using the report document class. MWE:

\documentclass{report}
\renewcommand{\thetable}{\Roman{table}}

\begin{document}

\listoftables
\newpage

\chapter{Chapter 1}
\begin{table}[htb]
    \centering
    \caption{This table is captioned with roman numerals, and is table number 1 in chapter 1} %This is Table 1.1
    \label{tbl:ch1t1}
\end{table}

\chapter{Chapter 2}
\begin{table}[htb]
    \centering
    \caption{This table is captioned with roman numerals, and is table number 1 in chapter 2} %so this is Table 2.1
    \label{tbl:ch2t1}
\end{table}
\end{document}

Previously, my table numbering convention (by the default that LaTeX uses) was that Tables 1,2,3... in chapter 1 would have table numbers 1.1, 1.2, 1.3,...

Tables in chapter 2 would have table numbers 2.1, 2.2, 2.3,...

However, with the \renewcommand{\thetable}{\Roman{table}} line, it gives the tables in sections 1 and 2 the same table number - I (because it resets the counter in between chapters). How can I generate a continuous set of table numbers so that the second table in the MWE has a table number of II?