I think you will find that Tony Richardson, Karel Reiss, and many others started by making films for under £20,000. The cameraman on The Zorro films and several of the Bonds, Phil Meheux, started off making films with friends and student actors.
What they did was to make movies for nothing - which, as I said, is perfectly possible. Werner Herzog stole his first 35mm camera and several cans of film. Others beg or borrow. And nobody pays student actors anything!
If the plumber had managed to get shown at a major film festival and got a distribution deal the story would have been different.
And that is the BIG IF!
As an unknown movie maker, you have to PAY for distribution, the theatre gets to keep all the box-office and you have to do the small, grotty festivals BEFORE you get to do anything important - and festivals nowadays cost real money! Distribution is like getting your widgets into major supermarkets - you hope and pray that never happens, because it can kill you!
If you happen to have £20k that is burning a hole in your pocket and you think that you are the next Quentin Tarantino, the first thing you have to do is to learn how to make movies. Not just the artistic side (though that is hard enough as it is and takes many years) but the technical side. Just the audio alone can make the layman's head spin. EBU standards. 5.1, 7.1, Atmos, DTS-X, dynamic range, all things that have to mean something to the movie maker.
Just reading the tech-sheets of TV play-out centres would have your plumber running for the hills!
But let us assume that our wannabe movie making plumber has got a close buddy that can oversee all the audio post-production tasks for him and that he has another buddy that can lend him an Arri Alexa and a set of lenses, grips, lights, hard-disks cables, microphones, etc. and he has access to a barn where he can build all his sets and rig lights and he has access to an editing suite and an audio post production suite where he can get all the foleys and ADR done and he has people on hand that can run all that stuff (actually students who are able to do all that and will do it for nothing do exist!) and assuming he has got someone on hand that can write and record a movie score (again, music students can be found under most rocks!)
Having climbed that very large mountain, our plumber has managed to put together a film crew without spending any of his £20k. He can still use that £20k for the one thing that outsiders to the movie industry always forget - Marketing!
Sadly, £20k won't get much, so he is going to have to do funky, off-the-wall, crazy things to get noticed and work social media as hard as he knows how. Any crazy and stupid stunt is legit. Just think of Pink Floyd's inflatable pink pig that mysteriously 'broke free' over Battersea Power Station! Stuff like that and more, much more. He might end up in a police cell for the night, but he will get publicity.
One of the best stunts is to launch a campaign to get his own film banned! Once the BBC has banned something or someone, success is assured!
One final tip for your plumber - make a quirky comedy and never ever go within 100 miles of a gritty urban drama. If someone comes at you with a script that features such lines as "Look out, he's got a knife!" or "Dad, I'm pregnant!" run, don't walk!