Shakespeare compared breasts to globes in The Rape of Lucrece, and used a globe in the punchline of a fat joke in The Comedy of Errors. The Pop-Up Globe that’s appeared in the grounds of Melbourne’s Myer Music Bowl serves a kinder purpose, if one no less Shakespearean. It will be staging four of Shakespeare’s plays and a contemporary work with a Shakespearean theme over the course of a repertory season that opens on 21 September and runs until 12 November.

The Globe, of course, was Shakespeare’s own famous London playhouse. Built in 1599, it was destroyed by fire in 1613, resurrected in 1614, and “closed by (the) ordinance” of the dastardly Puritans in 1642. By 1645, the history’s dullest religious zealots had had the vocational home of Britain’s greatest theatremaker razed to the ground to make way for tenement buildings. But one should never underestimate the patience of British vengeance; in 1997, a replica Globe was erected in London not too far from the original site and has served as a working theatre ever since.

Melbourne’s present pop-up owes its existence not to this theatre, so much as it does the depiction of the same in a picture book for children.

According to Miles Gregory, the artistic director and instigator of the Pop-Up Globe, the idea came to him while reading to his three-year old daughter. “The Globe popped up and she said, ‘Daddy, can we go there?’”. As they were living in Auckland, New Zealand, at the time, his initial answer was no. But Gregory had spent his “whole life fascinated by Elizabethan amphitheatres”, and had a collection of degrees in Shakespearean scholarship obtained from universities in Britain, so inspiration soon took hold.

Actors perform on stage at the the Pop-up Globe theatre in Melbourne. Photograph: Darrian Traynor/Getty Images

Using extant sketches of the second Globe made in the 1630s, Gregory sought to replicate not the replica, but the authentic experience of up close, stripped back Elizabethan theatre from the second Globe’s design.

“The project was big and exciting and seemingly impossible,” he says ... and it was completed in 15 months, just in time to coincide with Shakespeare’s 400th birthday celebrations in February 2016. He capitalised on the project by mortgaging his house, and with the support of a friend he’d known since he was four.

As a gamble, it’s paid off – the Pop-up Globe has completed two seasons in New Zealand, and already sold 40,000 tickets for its first repertory rotations in Melbourne. Three companies with a total personnel of 90 travel with the show, as does its wardrobe of 500 bespoke costumes. The size is warranted for the programme; no less than 14 individual shows are staged every week of its season. It’s a relentless schedule replicated in the physical construction of the theatre itself; the whole Pop-up is assembled over just six weeks, and packed down in less than three.

Miles Gregory sought to capture the authentic experience of up close, stripped back, Elizabethan theatre from the second Globe’s design. Photograph: Darrian Traynor/Getty Images

Those expecting the smell of the greasepaint and roar of the crowd to emanate from galleries of tiles and timber should be prepared. “This is not a lime and hair museum,” Gregory says. While the audience pit before the stage still demands its patrons stand, and the roof is every bit as open to the rain, the structure swaps the tiles of the original for corrugated iron and timber stalls for metal scaffolds – “honest material”, according to Gregory, and always sourced locally. Gregory’s own delight is in the strength of illusion conjured on his pared-down stage, its power over the audience. “They come to see the building,” he smiles, “but they come back … for the performances.”

Repeat viewings are affordable. Those wishing to experience Henry V, As You Like It, Much Ado About Nothing, Othello or Around The Globe in 60 Minutes can do so for standing tickets starting at $20.33. The fancy option of a somewhat royal-like private box is available from $150 with refreshments included. As previews begin this week, Melbourne, be aware: We the globe can compass soon / Swifter than the wandering moon.

• The Pop-up Globe season runs from 21 September to 12 November, with previews this week