Time for my Twopenneth worth!!
You mentioned you had a rubber bung!! this is part of a drain testing kit, by another bung a few tubes and a u tube and you could undertake an air test, from the Manhole internal manhole to the downside existing manhole.. obviously you need to have a period of running copious fresh water through the waste system to make the testing more agreeable.. you may then test up stream, but not certain how the wast from the sink could be made airtight for testing.
You havent said, but surely if this manhole is the source of the smells, then i would imagine on opening that cupboard door that the manhole is in, you should be hit with the sewer smell!!
Regarding blocking up this manhole, why not fit a few vertical battens to the side walls of the manhole with the tops level and as low down as possible cut a piece of ply as close to the shape as possible and insert to sit on batten ends, use a few tubes of mastic to seal the perimeter, and monitor for a day or two... if the smell persists then its probably not coming from the manhole base... it souds like you have had enough of it... but approach it methodically... putting upside down channel and concreting above seems fine idea... but that work may need to come out if the problem not cured, and that would be tough going.
As a matter of interest have you said smells appeared after builders... were there when you purchased?? if you did recent purchase what lebvel of survey was carried out??