"It must be made easier for hard-working Australians and Kiwis to visit and live in the UK," said Carol Driver, TNT's group editor.
"It is ludicrous that while Europeans can easily enter and stay in the UK, our Aussie and Commonwealth counterparts are being penalised.
"Let's hope Boris' words resonate with the PM and Home Secretary - and that these overdue changes are made to benefit the UK."
Mr Johnson, tipped by some as a future Prime Minister, has struck a chord with Kiwis on their OE after he said his government's immigration rules were disgraceful.
Writing in the Telegraph newspaper, Mr Johnson said Britain had betrayed its relationship with Commonwealth countries such as New Zealand, and advocated the establishment of "bilateral free labour mobility zones".
TNT Magazine has collected signatures for a petition calling on the UK Border Agency to improve its services, and has urged its readers to come forward with their own "horror stories".
The magazine heard tales of passports being held for up to a year, guests who had missed weddings, jobs nearly lost and people nearly deported because of wrong advice to those applying to extend British visas.
Ms Driver said one New Zealander is facing deportation after being told to apply for the wrong visa. This was despite having lived in London for nearly 10 years, being employed for that time and having a wife and two children.
A spokeswoman for the British Home Office told the Herald the country was building an immigration system that supported growth.
"We value our close relationship with New Zealand, which is based on our strong links through the Commonwealth and our shared history.
"The UK is open to the brightest and the best and we want to attract skilled migrants to the UK when they are needed by British businesses."
Reaction on the Herald Facebook page has been supportive of Mr Johnson's appeal, however some readers pointed out getting into New Zealand is not straightforward, either.
"The rules are just as tight here - six months max stay as a tourist or work permits to be renewed frequently at great expense if you have a family. This is not one way traffic!" Mark Connolly wrote.
Any citizen of a European member state can live and work in the UK.
New Zealanders can get a two-year working visa. If they wish to stay longer, they must qualify for an ancestry visa, or be classed as a skilled worker.
Brendon Watkins, with wife Michaela and children Courtney and Siobhan, wants to stay in Britain.
After a long and expensive battle with British authorities to be allowed to stay in the country, Brendon Watkins says he is losing his fighting spirit.
Mr Watkins, originally from the Bay of Plenty, is going into his ninth year in Britain. His South African wife Michaela has a British passport, and his two young daughters were born in his adopted country.
Although he meets all the criteria to stay, Mr Watkins' problems started when, he says, the UK Border Agency advised him to apply for the wrong visa. By the time the 36-year-old was told of the mistake, it was too late to receive the correct paperwork - some of which needed to come from New Zealand - before the deadline.
A bungled effort by his immigration lawyer added to the delay, and his application was refused because of time overspent.
"The last 10 years of our life has been put on hold ... To have it forced on you, to be deported - it's insulting, to be honest."
Mr Watkins has appealed against the decision, but it could be up to six months until a judge reviews the case.
In the meantime, if he leaves the country he loses the right to appeal.
That wait would not be a problem except that his father is battling cancer, and his grandmother has had a health scare.
"I desperately want to go home and see him ... I felt like writing [Boris Johnson] a letter myself. We should have a right to be here. It's quite a strong history, but it's all gone out the window."
• London Mayor calls for unlimited immigration from New Zealand.
• Backed by Kiwis in the United Kingdom, many frustrated by visa process.
• 4578 New Zealanders moved to UK for the long term last year.
