This worked out nicely. Few spots might be tricky, but not much.
Rules for Sudoku. Additionally, All neighboring cells which contain consecutive digits are separated by white dots.
Enjoy!
P341
PS : I LOVE old comedy shows! (Nothing relevant, more of a “dear diary” moment)
PS's puzzles + 
Mrm, this one seems to have 2 possible answers for the 5 and 6 in middle and middle left regions.
I am sorry for the late reply to this, I didn’t get a notification of the comment for some reason. I think you are missing the rule that implies all dots are given, which means, where there isn’t a dot separating two cells, they must be non consecutive. R3C1 (row 3, column 1) contains a 7 after solving, so 6 cannot be in R4C1 without a white dot between R3C1 and R4C1.
Don’t worry, I’m perfectly aware of that rule, I love this kind of Sudoku. 😀
Just.. now I actually see I’ve made a mistake somewhere else, whoops. Got a 7 and 9 confused somewhere, which’d explain why there is no 7 bordering the 5/6 spots, which made me get an ambiguous solution.
Thanks for replying, though!