Labour leadership contender Yvette Cooper and Scottish First Minister Nicola Sturgeon have joined thousands of people offering to house refugees.
Their pledge comes ahead of an expected government decision to allow about 20,000 migrants fleeing the Syrian war into the UK.
Prime Minister David Cameron said the refugees would come from camps neighbouring the Middle East country, rather than areas of Europe where thousands were already seeking asylum.
Mr Henderson said: “Obviously, we’ve all been touched by some of the pictures we’ve seen on TV screens.
“I think the Prime Minister’s suggestion we take in refugees direct from camps in Syria probably strikes the right balance – but we can’t take in unlimited numbers in the way some people are suggesting we ought to.”
The MP said that in the long-term “putting money” into war-torn countries would “ensure they become more safe and economically viable and make it less attractive for people to have to come to Europe”
Gordon Henderson is a regular guest on BRFM Daytimes.