Conversion therapies could be made into a criminal offence as part of government measures to ban the practice within months.
The move would also ensure individuals found guilty of the practice cannot profit from it, the GEO said.
It has launched a six-week consultation inviting views on how to legislate against the practice of trying to change someone's sexuality or gender identity through counselling.
Ministers will legislate to ensure that, when existing violent offences are motivated by conversion therapy, it is considered as a potential aggravating factor when the perpetrator is sentenced.
The proposed new offence for talking therapies would be punishable by imprisonment of up to five years and would apply to under-18s under any circumstance and to adults who have not freely consented and been fully informed about the potential impacts.
The GEO said consent requirements would be "robust and stringent" and acknowledged that some people believe an adult cannot consent even when fully aware of the risk.
It added the government's view is that "the freedom for an adult to enter such arrangement should be protected".
Any future law would place emphasis on protecting children and ensure regulated clinicians can continue their work with people who may question if they are LGBT+, the GEO said.
Simply expressing the teachings of a religion will not constitute conversion therapy and cannot be "reasonably understood" to include casual conversations or private prayer.
It said it will continue to work with faith communities to develop an approach that protects people while respecting the right to freedom of religion and belief.
Minister for Women and Equalities, Liz Truss, said: "There should be no place for the abhorrent practice of coercive conversion therapy in our society."
She said the proposals would ensure LGBT+ people "can live their lives free from the threat of harm or abuse".
"I want everyone to be able to love who they want and be themselves," she added. "Today's announcement sets out how we will ban an archaic practice that has no place in modern life."
The government also plans to introduce civil measures such as Conversion Therapy Protection Orders, which could include removing the passports of potential victims at risk of being taken overseas.
It will also explore ways to prevent the promotion of conversion therapies, including online.
It will fund a support service for victims and those at risk of conversion therapy and is launching a tender process in November.
However, critics say the plans don't go far enough - and argue all types of conversion therapy should be outlawed.
Nancy Kelley, Stonewall chief executive, welcomed the action but warned there were still concerning loopholes, including on prayer.
"We also can't support the proposals that allow for people to 'consent' to conversion therapy - a practice that is abusive cannot be consented to. If we are to truly put this shameful practice behind us, the ban must not allow for any excuses or any exemptions," she said.
Shadow women and equalities secretary Anneliese Dodds said: "It's astonishing that these proposals leave the door ajar for people to 'consent' to these insidious practices on religious grounds. In contrast, Labour would implement a genuine ban on conversion therapy immediately and outright - to keep LGBT+ people safe."
The consultation will close on 10 December and legislation will be introduced by spring 2022.