Craig Williams, MP for Montgomeryshire, has written to Shrewsbury MP Mr Kawczynski asking him to rethink his criticism of the Welsh Government over its policies to tackle the coronavirus crisis.
Mr Kawczynski had accused Welsh First Minister Mark Drakeford of undermining the Prime Minister's message over the virus, after Mr Drakeford said there would be no relaxation of the lockdown restrictions in Wales.
He said having different laws in England and Wales caused difficulties in border areas such as Shropshire and called for a rethink over the "expensive and unnecessary" Welsh Parliament.
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"The Prime Minister has told us we can go to the beach now, but we are then told we can't go to any of our closest beaches because they are in Wales, and the Welsh Government doesn't want us to come," Mr Kawczynski said.
"There are some golf courses in Shropshire which are half in Wales and half in England, and we need a cohesive policy which covers the whole of the country. At a time of national crisis, people expect to hear a single, united voice."
Mr Kawczynski said there were other areas, such as transport and health, where the divergence of policy caused problems for border communities.
"I'm happy with the Prime Minister's statement, but worried what the Welsh Assembly is doing to cohesion of Britain," he added.
Mr Williams said that while he shared some of Mr Kawczynski's concerns, MPs had to respect that the devolved Welsh Government would want to exercise its powers.
He wrote: "The time for serious debate and inquiry into the effect of this divergence is not for now. It will come later. In the meantime, to question the fundamentals of Welsh democracy because of any divergence is wrong and unhelpful."
Mr Kawczynski said he fully respected Welsh democracy, but wanted to open up a respectful debate about whether having two different sets of laws for communities that were closely intertwined were good for the areas affected.