How exactly do you want it to work? At what point (what percentage of the electorate voting NOTA) would action be triggered, and what would that action be?
The pertinent question to ask @WhatWouldJeevesDo . I don't think those suggesting this have thought that far ahead.
Looking into it a bit further
Here's their website https://nota-uk.org/ which tell us they've been around since 2012. So appear to have achieved absolutely nothing over the past twelve years. Although do seem to have a gift for exaggeration. Just not communication or the ability to influence people and bring about change.
They reference a report from the https://committees.parliament.uk/committee/200/political-and-constitutional-reform-committee/publications/
This is the Committee's 2014-15 session which amongst other things did recommended recall petitions - which has come to fruition as we've seen in a number of recent by-elections. The report recommendations did not however extend to adding NOTA on election ballot papers.
That said the report https://publications.parliament.uk/pa/cm201415/cmselect/cmpolcon/1128/1128.pdf
does make reference to work they did on voter engagement and an interim report on that published in November 2014 https://publications.parliament.uk/pa/cm201415/cmselect/cmpolcon/232/23202.htm. That link just then provides further links to individual chapters and sections, but not, as far as I can see a single link to the full report. Anyway the conclusions https://publications.parliament.uk/pa/cm201415/cmselect/cmpolcon/232/23211.htm does make an important observation ...........These are all legitimate reasons for people to disengage from the electoral process, and it cannot be said that low turnout levels and registration rates are the result of apathy on the part of the public
Scroll down far enough - I've saved everyone the pain of having to do so - and you'll find
51. We recommend that, in the event that voting in certain elections is made compulsory, an option to vote "none of the above" or to "abstain" should be one of the options set out. These options could also be included even if voting were not compulsory. (Paragraph 178)
Paragraph 178 is simply copied verbatim from another section of the report, with that then including para 176
176. A number of written submissions recommended that there be an option for "none of the above" on the ballot paper if voting were made compulsory—so that people were not compelled to vote for one of the candidates standing for election—and others supported the option of voting formally for "none of the above" on the ballot paper, whether voting was compulsory or not.[401] A written submission from Nota UK stated that being able to vote for "none of the above" would allow people to actively withhold consent from the parties standing for election.[402] Being able to vote for none of the above was the most popular choice by 38 Degrees members in their survey of "What would make you more likely to vote in the 2015 General Election?", picked by over 18,000 of the 84,000 respondents.[403]
However the outcome despite all the tortuous content above was that NOTA did not as stated earlier feature at all in the Committee's ultimate recommendations.
There was a parliamentary petition started earlier this year. With the public lack of interest such that it had only received just over 6,000 signatures when it, like all other live petitions, was stopped when the July GE was called.
https://petition.parliament.uk/petitions/650023
The wording of the petition gets back to your original question, but as you might have guessed already raises more questions as opposed to any answers.
I urge the UK Government to permanently adopt "None of the above" on all ballots starting with the next general election, to enhance democratic choice and allow voters to express dissatisfaction. If NOTA wins most votes, consider rerunning the election, possibly with initial candidates disqualified.
Sadly it does not give away whether that will be all elections, or a specific election such as the GE; or indeed whether it would apply to the overall result, or individual constituencies. Or is there is some sort of NOTA victory margin needed - what would consider rerunning be defined by? Or get into any of the implications of delayed results, or the simple practicalities and logistics of re-running an election. Presumably a month or so gap would be needed to re-issue voting cards, postal votes; re-book spaces to be polling stations; arrange all the staffing needed for polling stations and the count. Just minor details like that. And find new candidates if the originals are somehow disqualified. And what would happen then if NOTA won again, would the election continue ad infinitum. And that's before we get into costs of running an election.
Not convinced any joined-up thinking has been applied. Reality detachment on a grand scale.