Here is another suggestion that still works if there is an unnumbered chapter or an unnumbered part or an appendix.
\documentclass[
chapterprefix,
%numbers=noenddot,
%toc=indentunnumbered,
%listof=totoc,
%listof=chapterentry
]{scrbook}
\usepackage[english]{babel}
\RedeclareSectionCommand[
tocnumwidth=4em
]{part}
\RedeclareSectionCommand[
tocnumwidth=6em
]{chapter}
\RedeclareSectionCommand[
tocindent=6em
]{section}
\RedeclareSectionCommand[
tocindent=8em
]{subsection}
\let\oldaddchaptertocentry\addchaptertocentry
\renewcommand{\addchaptertocentry}[2]{%
\ifstr{#1}{}{%
\oldaddchaptertocentry{#1}{#2}}{%
\oldaddchaptertocentry{\chapapp{} #1}{#2}%
}}
\let\oldaddparttocentry\addparttocentry
\renewcommand{\addparttocentry}[2]{%
\ifstr{#1}{}{%
\oldaddparttocentry{#1}{#2}}{%
\oldaddparttocentry{\partname{} #1}{#2}%
}}
\usepackage{blindtext}
\begin{document}
\frontmatter
\tableofcontents
\listoftables
\chapter{This is a chapter in frontmatter}
\mainmatter
\part{This is a part}
\blinddocument
\begin{table}%
\begin{tabular}{l}
\Huge X
\end{tabular}
\caption{A table}
\end{table}
\addchap{This is an unnumbered chapter}
\addsec{This is an unnumbered section}
\appendix
\blinddocument
\end{document}
Result:

Update using KOMA-Script Version 3.20 (or newer)
\documentclass[chapterprefix]{scrbook}[2016/05/10]
\newcommand\partentrynumberformat[1]{\partname\ #1}
\RedeclareSectionCommand[
tocentrynumberformat=\partentrynumberformat,
tocnumwidth=4em
]{part}
\newcommand\chapterentrynumberformat[1]{\chapapp\ #1}
\RedeclareSectionCommand[
tocentrynumberformat=\chapterentrynumberformat,
tocnumwidth=5.5em
]{chapter}
\RedeclareSectionCommand[tocindent=5.5em]{section}
\RedeclareSectionCommand[tocindent=7.8em]{subsection}
\usepackage{blindtext}
\begin{document}
\frontmatter
\tableofcontents
\listoftables
\chapter{This is a chapter in frontmatter}
\mainmatter
\part{This is a part}
\blinddocument
\begin{table}%
\begin{tabular}{l}
\Huge X
\end{tabular}
\caption{A table}
\end{table}
\addchap{This is an unnumbered chapter}
\addsec{This is an unnumbered section}
\appendix
\blinddocument
\end{document}

\addchapcommand in the document or an chapter in\frontmatter. It results in anChapter .before such an unnumbered chapter entry in TOC. – esdd Feb 27 '16 at 20:14