Both the MPs for Weston and North Somerset have called for a less stringent approach from the UK to grant Ukrainians refuge from the Russian invasion.
Current Government policy has been criticised as it does not allow Ukrainians without an immediate British national family member or Ukrainian nation settled in the UK to apply for a UK family migration visa.
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North Somerset MP, Dr Liam Fox told BBC News that Parliament's general view is that the UK will 'have to play its full role in helping' with the crisis.
Dr Fox said: "The Ukrainian refugee crisis will clearly have to be done in the same way we coordinated international sanctions against Russia and that all countries in the free world are playing their part - not just in Europe.
"The priority has to be that we have a predictable and workable system which is not marred with the chaos we have seen in previous conflicts.
"I think the current policy will have to go wider - we are at the beginning of what may be a big refugee problem and we'll have to think through how we are all going to handle it. Of course, refugees might not want to go to countries beyond central Europe and may want to stay in countries such as Poland."
MORE: How to support Ukraine from Weston.
The EU has announced that it will be accepting refuses across its borders with no applications required to stay for up to three years.
The former Defence Secretary added: "We will have to include more refugees to enter through our policy.
"There is always a possibility of Putin pulling back and stopping this slaughter though it may be too late for Putin in terms of committing war crimes."
Weston's MP, John Penrose, also expects the UK government to go further with its policy in the coming days though believes we should err on the side of caution.
Mr Penrose said: "This week saw a huge expansion in the number of Ukrainian refugees who will be able to come to live in the UK, with about 100,000 more places created.
"I expect our Government to go even further in the coming days, although we’ve got to be careful to target places for imperilled Ukrainians without throwing open our borders to anybody from other countries - including potential Russian agents.
"And I was pleased to see North Somerset Council’s pledge to welcome refugees displaced by the conflict too."
North Somerset Council has previously stated: "We stand ready to welcome refugees displaced by the conflict.
"We will also do what we can to avoid purchasing items or services supplied from Russian companies, given the flagrant law-breaking of their own state, and we urge all other local authorities to do the same."
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