Senior Tories have piled pressure on Theresa May to allow safe injection rooms for drug users in an effort to prevent drug-related deaths and reduce HIV infection rates.

They are among the heads of five cross-party parliamentary groups calling for the government to lift the block on drug consumption rooms (DCR), in a campaign organised after concerns raised by the National Aids Trust.

Advocating for the UK’s first such facility, which would enable those to inject illicit drugs under the medical supervision of trained staff, they urge ministers to make the opening of a DCR an “urgent priority” in Glasgow.

According to the National Aids Trust, there is currently an “ongoing and extensive” outbreak of HIV among those who inject drugs in the region.

The charity claims that efforts to curtail the outbreak have been “hindered” by a number of issues but in particular the government’s refusal to open the drug facility.

When pressed on the issue last month by the SNP, the prime minister told MPs the government “had no plans” to introduce any such facility, with her focus being on treatment and recovery.

In a letter seen by The Independent to be sent to Sajid Javid, the home secretary, on Monday, the chairs of the parliamentary groups write: “The position from the government to date has been simply to insist on the unlawfulness of drug consumption rooms under the Misuse of Drugs Act 1971.

“We strongly believe a more open-minded and innovative approach is urgently needed to save lives and prevent the spread of blood-borne viruses such as HIV.”

The signatories are the chairs of five All Party Parliamentary Groups (APPGs), and include the Conservative MPs Crispin Blunt and David Amess and Labour MPs Jeff Smith, Mary Glindon and Stephen Doughty. Three crossbench peers and two Liberal Democrats peers have also given their backing to the campaign.

They are calling for an amendment to be made to the 1971 Misuse of the Drug Act in order to allow a drug consumption room to open in Glasgow.

The letter continues: “We believe the opening of a DCR in Glasgow is an urgent priority.

“In the short term, we request the home secretary takes the same approach as they recently announced with festival drug testing, by sending a message that local police and crime commissioners and health authorities can develop their own positions without direction from Westminster. This would allow a DCR to open promptly.”

Deborah Gold, the chief executive of the National Aids Trust, told The Independent: “A wealth of evidence shows that drug consumption rooms significantly reduce sharing of injecting equipment (and blood-borne virus transmission), as well as reducing overdoses and drug-related deaths.

“There are now over 100 cases of HIV linked to this outbreak and unless the UK government allows Glasgow to take a more innovative approach that prioritises harm reduction, efforts to tackle this outbreak will stall.

“We call on the government to rethink their position and allow a drug consumption room to open, which will support efforts to tackle the HIV outbreak and will also save lives.”

It comes after Alison Thewliss, the SNP MP, raised the issue in the Chamber at the last prime minister’s questions before the summer recess.

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“There were 934 drug-related deaths in Scotland last year. Each one of those deaths is a tragedy, and a preventable one at that. Drug laws are reserved to Westminster,” she said.

“How many more families is the prime minister willing to devastate before she will allow Glasgow to get on with the work of building a drug consumption room to save lives?”

While Ms May responded by saying that each death due to drugs is a “tragedy”, she said there is no legal framework for the provision of drug consumption rooms and that the government had “no plans to introduce them”.

The prime minister added: “A range of offences is likely to be committed in the operation of drug consumption rooms.