Theresa May said that approach would prevent others from making the journey.
Hundreds have died trying to get from north Africa to Europe on makeshift boats so far this year.
But Dave Smith from the Boaz Trust, a group supporting asylum seekers in Manchester thinks many travelling have no choice due to circumstances in the countries they are travelling from.
Speaking on Premier's News Hour, he said: "I think it's unfortunate, I think it's a little bit inflammatory and I believe she's actually misguided.
"She's always said that there's some sort of pull factor but in reality most of the people coming on those boats are not being pulled they're being pushed, so I think she's wrong basically."
The European Commission's voting on whether to force member states to accept asylum seekers who make their way across the Mediterranean but Theresa May says the Government will reject any EU proposals for a mandatory system of resettlement in Britain.
The Commission first vice president says they have to put forward new proposals because doing nothing will only make the situation worse.
Dave Smith is keen for people to hear the full story on why people travel. He said: "The reality is that you have to pay a smuggler, you have to pay an agent, to get you out of these countries.
"Because as far as I'm aware there's nobody from our country's actually gone over there and offered them safe passage."
He stressed that these people are fleeing dire situations: "There will be some who you could term economic migrants I guess.
"But when you look at the people actually making up the folks on the boats - a large number of them are from the Horn of Africa - from Eritrea, from Somalia, from Sudan.
"And these are people particularly the Eritreans who are fleeing absolutely horrendous conditions in their countries - where there's forced conscription from the age of about 18, you can be conscripted for thirty or forty years with no chance of getting out.
"If you're a Christian you'll be severely persecuted if you live in that country, so people are fleeing horrendous situations - they haven't come for the good of their health or to get a better life."
Listen to Premier's Marcus Jones speak with Dave Smith on the News Hour:
