St Augustine's Centre says recent relaxations of visa requirements for Ukrainians do not go far enough and have criticised the Government for pressing ahead with the "cruel" Nationalities and Borders Bill.
"Just over six months on from the fall of Afghanistan to the Taliban, we find ourselves once again watching in horror as a humanitarian crisis continues to escalate," said the charity.
"Once again, we are reminded of just how quickly people can find themselves fleeing for their safety. And once again, we watch as the UK government fails to act with urgency, flexibility, or compassion.
"Whilst Boris Johnson continues to make empty promises of protection and assistance for those fleeing the war in Ukraine, the Government presses on with the cruel Nationality and Borders Bill - a piece of legislation that fundamentally dismantles asylum rights under international law.
"The Home Secretary’s recent announcement of relaxed visa requirements also fails to go far enough. The rules for those with family members within the UK remain too strict and the process too lengthy to provide the type of immediate relief and support the people of Ukraine need.
"Furthermore, it’s still unclear how the community sponsorship scheme will work or how long it will take to establish.
"We join other British charities in urging our Government to protect those fleeing any violence in Ukraine and to follow the UNHCR's call to keep borders open for those that need our help.
"We also call on the Government to commit to an emergency resettlement programme, as an expected four million people from Ukraine become refugees.
"We are also urging the Government to rethink its flawed Nationality and Borders Bill, which would treat people forced to make dangerous journeys to seek safety on our shores as criminals.
"We must play our part in helping the people of Ukraine seek safety and support, whilst ensuring future protection for others forced to flee their homes."
Next Thursday (March 17) the charity is inviting people to join them at The Piece Hall and help them create giant heart shape which will be captured by drone photography to share as part of a national show of support for refugees.
"We need a lot of people to make it work, so please bring your friends and co-workers. Wear orange if you can - you're also welcome to bring your own orange heart or sign," said the charity.
The event takes place at 9am and will be finished by 9.30am. People should enter via the Westgate entrance. Any questions, call Amber on 07484 665044.