A Covid-19 recovery strategy and partnership update was given to Carlisle City Council at a meeting of the authority's health and wellbeing scrutiny committee.
Councillor and committee chairman Jack Paton asked if contingency plans were in place to fight off a spike in infections as cases are rising across the border.
Cllr Paton said: "Our neighbours across the border, there's reports that Covid seems to have increased quite dramatically and it is a big concern because we're very close to them. Do we have anything in place in case it spreads over the border and it comes back into Cumbria? Do we have any sort of strategy for that?"
Steven O'Keeffe, policy and communications manager said: "You'll appreciate that the weekly figures are published on the county council website. I think even in the last narrative report there's a reasonable stable number but relatively high number of cases in Cumbria but below the national average.
"I know that the director of public health, senior managers, talk about cross border issues and keep a close eye on potential spread of infection across different communities."
Councillor Elizabeth Mallinson said: "I sit on the public health alliance and it's now very slimmed down because we are very focussed. We have a communications team which is hosted by county council and we are looking at all the cross border, not only north but east and south.
NASUWT- The Teacher's Union has called on the Government to step up measures to control Covid-19 in schools due to the rise in cases seen in Scotland and Northern Ireland.
The union wants to see proactive measures around ventilation and the extension of on-site Covid-19 testing as the rise in cases comes just as pupils return to school from Summer holidays.
Dr Patrick Roach, NASUWT General Secretary, said: "Ministers must not risk complacency or follow a strategy of crossing their fingers and hoping for the best if the number of Covid cases rises following school reopening."
"We only need to look across the border to Scotland to see that there has been a steep increase in Covid cases among school-age pupils within just a couple of weeks.
"In the event of rising case numbers, Ministers will need to consider the reintroduction of the requirement for pupils to self-isolate when they have been in close contact with someone who has tested positive.
"This should be supported by an extended programme of onsite testing in schools, rather than relying on a less effective system of home testing.
"Schools will also want confirmation of the timetable for the rollout of already promised Co2 monitors into schools to assist them in ensuring good ventilation.
"There is no reason for further disruption to pupils' education, where sensible and proportionate measures are taken to support the already tremendous efforts being taken by schools and staff."