The sanctions target five Russian banks, which have had their assets frozen in Britain, and three Russian billionaires, who will be hit with UK travel bans.
However, several MPs do not believe the Government has gone far enough.
In the House of Commons on Tuesday, Mr Perkins said the Government has ‘started from the point of saying, ‘here’s some sanctions. We know you’re going to do more. And when you do more, we’re going to do more’.
“The message coming from this place could not be much feebler,” he added.
Addressing Foreign Office minister James Cleverly, Mr Perkins said: “Will he ensure that (partners in the west) know that the resolute opinion of this house is that the sanctions that have happened so far are only a start, and that much stronger action needs to come for the sake of Ukraine and for the sake of President Putin getting that message?”
Mr Cleverly responded: “I give ... members the absolute assurance that we regard these measures as the start of a range of sanctions that we can escalate in response to what Russia does.”
And on BBC Breakfast on Wednesday, Foreign Secretary Liz Truss said the sanctions were the most severe the UK had ever placed on Russia.
She said it was important to keep further sanctions ‘in the locker’.
"We’ve shown we are united and we will escalate those sanctions in the event of a full invasion into Ukraine,” she added.
Meanwhile, on Twitter, fans of Chesterfield FC in Ukraine have thanked local people for their support.
The Ukrainian Spireites account posted: “We are overwhelmed by incredible support from our Spireite friends, including active position of @tobyperkinsmp.
“My granddad, who was a miner and later became a politician, would be proud of this strong bond between us and our special friends.
“We would like to thank you.”
Putin – who has denied he has any intention of invading Ukraine – has made clear he sees Ukraine’s aspirations to join NATO, a military alliance comprising of 30 nations, as a threat to Russia’s borders and its sphere of influence.
On our Facebook page, we asked people how concerned they were about the current situation regarding Ukraine and Russia, and if they thought the UK should get more involved in the crisis.
Councillor Ross Shipman said: “I always look at these situations from the point of view of ‘what would I want the world to do if my country was being invaded by hostile forces’.
“In a global world, sitting on our hands while Russia keep carrying out aggressive acts against sovereign nations is not an option and doesn’t seem like a British thing to do.”
Anne Jones said: “Putin is a very dangerous man. I find this all very worrying.”
But David Brocklehurst said: “Keep out of it. Why is it every time other countries start war, we have got to stick our noses in their affairs.”
Brenda Rimington added: “We have enough going on here.”