Conservative MP Christopher Chope blocked the bill at Friday's session to cries of "shame" from other lawmakers but Hobhouse has asked for it to be debated on July 6.
Today, ministers have confirmed that the Government will support legislation to close any potential loopholes, in order to better protect victims and increase convictions.
"This behaviour is a ugly invasion of privacy which leaves victims feeling degraded and distressed", said Frazer announcing the government's backing.
"I think it's very frustrating and annoying that one MP can block a consensus that had been built over several months", she said.
Chope has long campaigned against Private Members' Bills, believing that only those appointed by the Prime Minister should be able to introduce legislation.
A government spokesman said: "Whilst we are disappointed this Bill did not pass second reading today, we look forward to supporting these measures through the House at the earliest possible opportunity".
Even then, it would only take one dissenting voice to again put a stop to its progress.
Ms Martin, who has faced rape and abuse threats since launching her campaign, said she was "extremely upset and disappointed" by Sir Christopher's decision.
She said making upskirting a specific offense would send a clear message that perpetrators will be punished.
Martin's next step is to meet with Tory MP Lucy Frazer, along with Hobhouse and her lawyer Ryan Whelan to plan their next steps. Four of the 26 bills that fell at the same time were my own. Lorna Rees, who lives in Sir Christopher's constituency of Christchurch in Dorset, vented her anger at him by draping home-made knicker bunting outside his door (pictured, right).
Victims of upskirting have been found to be as young as 10 years old.
Under the new legislation, which will have its second reading in the House of Commons, perpetrators would face up to two years in jail and the most serious offenders would be named on the sex offenders register.
However, ministers have chose to act after concerns were raised that potentially not all instances of "upskirting" are covered by existing criminal law.