Donations for Ukraine are being collected at a pop-up community centre in west London
"I've been losing sleep over it," says 32-year-old Joseph, whom we are only identifying with his first name at his request after he said he planned to make the journey to help in any way he can. "I feel like we're not doing enough."
Although he says he has recently applied to join the British army, he does not have any military experience - and has no links to Ukraine other than a friend he attended college with.
After hearing Mr Zelensky's appeal, he has come to a pop-up Ukrainian community centre in Holland Park, west London, set up to receive donations. But his search is for Ukrainians who might give him information on how to enlist for the war effort.
"I understand how tense the situation is and I understand what we're trying to avoid, [but] I think we need to stop [Putin] in his tracks. If we won't properly assist Ukraine then people are just going to have to volunteer and hope that we can have some kind of impact even if it's small."
Although Foreign Secretary Liz Truss did say in a BBC interview on Sunday she would support those in the UK who wanted to take up arms in Ukraine, the government has since made it clear that is not the official policy.
The most recent statement issued on the subject reminds people that the Foreign Office currently advises "against all travel to Ukraine". and "the best way we can help Ukraine right now is by ensuring Putin fails".
MP Tobias Ellwood, who has served in the Army and is chairman of the Commons defence select committee, was unequivocal on Twitter as he wrote: "Please do NOT go if you have no combat experience. You may get yourself, and others who have to look after you, killed."
But Joseph says he is not deterred: "I've got friends who have been in the service, so I've got an idea of what to expect. I've had my warnings."
He said the reaction from his family has been mixed, but they can understand his reasons for wanting to volunteer.
"The stance is, if you believe in something, if you genuinely believe in something - like freedom, a democratic system - unfortunately you've got to be willing to die for it," he says.
"We live a short life, let's make it count."
The Ukrainian embassy told the BBC it appreciated the support of "all people who want to support our country and fight Russian aggression",but it stressed it was playing no role in helping people enlist.
Instead, informal networks have emerged to help put Britons in touch with people who can meet them in third-party countries between here and Ukraine and assist them in getting to the front line.
Luke, 22, a Londoner who also has no military training, admits he is scared by the prospect of going to Ukraine, but still plans to make the journey.
"I feel like just watching the news everyday and seeing what's happening, I feel like I want to help in some way," he says.
"So if I can then I will. Even moving things around, driving, anything. I want to help in any way I can.
"If a 22-year-old fit and healthy person isn't going to go, who is going to go and defend them?"
He says he is hopeful that foreign fighters can help make a difference in the conflict.
"I think it's amazing what the Ukrainians have done so far without… [Nato] troops on the ground," he says.
"So I do think eventually, if enough people go to help, and we do keep supplying aid to them, lethal and non-lethal, then we can push them back."
He also says he hasn't told his family about his plans to travel to Ukraine and doesn't intend to before he leaves. "I don't want anyone to talk me out of this. I've made my decision," he says
Of course many of those who are planning to travel from the UK are Ukrainians who are not affected by the Foreign Office advice and can freely choose to return home. Among them is Mykhalo, a 43-year-old from the city of Lviv who was on a visit to the UK when the invasion started.
He normally works in building management and has no military experience, but wants to get back as soon as possible to join the fighting.
"It might be tonight, who knows. I just must help my country. I have no choice," he says.
"We are not the richest country. But we never affected any other country. People have normal life. Working, working, cooking, laughing, travelling. And now, some monster… I don't know what he's thinking about."
Asked what he thinks about the British nationals volunteering to help defend Ukraine, he says: "My brothers! I love them."
The community centre has been receiving a steady stream of donations of military equipment as well as food and clothing for people displaced by the conflict.
Ewan Vidion has just delivered a carful of items donated by reservists and others from around Portsmouth and South Hampshire.
"What I've brought is what they're urgently in need of," he says. "It's the medical supplies, the field dressings and also military gear, military clothing, bergens [military backpacks], mats for them to sleep on, some helmets."
The plan is for the donations to be packed into a convoy and transported overnight to arrive in Kyiv on Thursday.
Ewan says: "People feel like our hands are tied, so it's a case of saying 'What can we do as ordinary people?'"