Will Quince says disruption should be expected during planned walkouts from paramedics on Wednesday.
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A health minister has urged people to avoid “risky activity” during a planned strike from ambulance workers on Wednesday.
Will Quince said those in need of emergency help should continue to call 999, but disruption to services was inevitable.
Around 750 armed forces staff are being drafted in to cover the walkouts in England and Wales.
Mr Quince said ambulances should still respond to the most serious calls.
Speaking on BBC Breakfast, he said ministers wanted category 1 and 2 situations, including cardiac arrests and strokes, to be covered.
Health Secretary Stephen Barclay will meet unions later to discuss staffing levels during the strikes.
Mr Quince said the military staff drafted in for Wednesday would provide “support capacity” for individual NHS trusts.
He added that they would not be able to drive ambulances under blue lights, go through red lights or break the speed limit – but would help ambulance staff to get people to A&E more quickly.
Health chiefs have warned of “extensive disruption,” and urged hospitals to free up beds by safely discharging patients ahead of industrial action.
Measures should also be put in place to make sure ambulance patient handovers are kept to no more than 15 minutes, they advise.
Mr Quince said the government expected category 1 and 2 calls to be responded to. As well as cardiac arrests and strokes, these categories also include heart attacks, serious burns, and compound fractures, he said.
Taxi bookings
He added that for less serious categories, NHS trusts would be block-booking taxis to take people to hospital, and “encouraging people wherever possible” to find treatment by making journeys themselves.
“There will be disruption to service. It is important that where people are planning any risky activity, I would strongly encourage them not to do so,” he added.
Decisions on staffing are being taken on a local basis, meaning there will be potential variation in service by region.
Wednesday’s action will involve members of the Unison, GMB and Unite unions. GMB members are also due to on strike again on 28 December.
Unions representing NHS staff in England and Wales are pushing for higher pay after being offered a below-inflation average 4.7% rises this year.
Unison has said troops are “no substitute for trained ambulance staff” – and a rethink on NHS wages from the government could have averted action.
The strike will follow strikes from nurses on Tuesday in England, Wales and Northern Ireland, who are taking their second day of action this month over pay.