You might be interested in mixed member proportional voting. It's not exactly what you described, but similar in philosophy. It has FPTP elections and then a second round of regional electors which compensate for the disproportionality of of the first round. It doesn't achieve perfect proportionality and is potentially open to abuse by some methods involving puppet parties, but it mitigates a lot of the issues with FPTP
Seeing as you referenced the UK Labour Party you might already know this as the system used in the Scottish and Welsh assemblies