Gloucestershire Constabulary said it would be questioning drivers and “encouraging them to turn around” if they do not have an exception to current travel restrictions.
If people refuse, officers will pass their details to Welsh police forces to consider issuing a fine.
The operation was announced after North Yorkshire Police was criticised for setting up road checks at the start of the UK’s coronavirus lockdown in March.
It later emerged that the government’s guidance on “essential travel” could not be enforced, and there was no law against people travelling long distances for exercise and recreation.
Under Wales’ 17-day firebreak lockdown, which began at 6pm on Friday, people can only travel for “essential” reasons such as caring responsibilities and work.
The Welsh government website says that people cannot go on holiday in other parts of the UK that are under less severe restrictions.
But police in England can only enforce the laws in place in their areas, and the wrongful application of Welsh laws has already resulted in numerous lockdown fines and prosecutions being overturned.
Guidance issued to police officers also states that they have no power of “stop and account”, meaning they cannot compel people to answer questions on where they are going and why.
A spokesperson for Gloucestershire Constabulary said: “While we cannot issue fines to those travelling from Wales into the county, we can inform the host force of those we stop about what has happened so they can take action.
"Officers will be running an operation over the weekend that will cover routes from Wales into the Forest of Dean and if we stop someone travelling from Wales we will be engaging with them to find out why, explaining the legislation and encouraging them to turn around if we are not satisfied with their explanation.
“If they don't turn around we will then inform the force that polices the area they have travelled from so that they can issue a fine.”
The National Police Chiefs’ Council said the operation was a “force issue” and not part of national policy.
Avon and Somerset Police, which also borders Wales, said it had no plans to run a similar operation.
“Any calls we receive which are directly linked to the restrictions currently in place in Wales will be assessed on the threat, harm and risk posed to the public and given the appropriate level of response,” a spokesperson added.
Cheshire and West Mercia Police have not yet responded to The Independent’s request for information.
Under the Welsh restrictions, people can only leave their home for limited reasons, such as to buy food and medicine, provide care or take exercise, and they must work from home where possible.
All non-essential retail, leisure, hospitality and tourism businesses are closed, along with community centres, libraries and recycling centres, while places of worship are shut other than for funerals or wedding ceremonies.
The Welsh health minister, Vaughan Gething, said the firebreak lockdown will give people the ”best chance“ of seeing each other over Christmas.
He told BBC Breakfast that scientists believed the lockdown would reduce the R value - the number of people each coronavirus case infects - to below one.
”In acting now, we're both arresting what we know will be harm coming into our hospital system, arresting the number of deaths we could otherwise expect, giving us a better opportunity to have a national set of measures that people can and will follow,” the minister added on Saturday.
Andrew RT Davies, shadow health minister for the Welsh Conservatives, was among those who criticised a ban on the sale of non-essential items including greeting cards, toys and books.
“I never thought I'd live in an era where aisles in supermarkets were blanked off because you couldn't buy hairdryers or you couldn't buy baby clothes, or toys for children, when the store is open,” he said.