A statement issued by Foreign Office spokesman Moazzam Khan said the government "strongly condemns the attack" on Almeby, who was "critically wounded in Lahore".
"The government will undertake a thorough investigation into this criminal act and make all efforts to bring the perpetrators to justice," the statement said.
"Our thoughts and prayers are with the family of Ms Almeby," it said.
Almeby, who works for the Full Gospel Assemblies of Pakistan, was shot by two armed men while she was returning to her home in Lahore yesterday.
Her organisation has described the incident as a "targeted" attack.
No group claimed responsibility for the incident.