Hume also called for ministers to “really look at what happens when fire gets close to a piece of critical national infrastructure”.
Last summer’s wildfire burned near to RAF Fylingdales, part of the UK and US ballistic missile warning system.
She said she had visited the site this week and spoke to staff who “can’t just turn the radar off and leave”.
“It was quite sobering to hear how worried they were as the fire got closer.”
Last month, a wildfire in Suffolk was about 3 miles (5km) from the Sizewell B nuclear power station.
Hume said such situations should automatically trigger national resilience, when firefighters from brigades around the country are sent to assist.
“Extra resources come in at that point where something as important as RAF Fylingdales is threatened by wildfire because it’s literally in the middle of a moor, it’s very vulnerable,” she said.
On Friday, Burnham said Britain was a “tinderbox” and outlined plans to expand support for fire services and ensure they are properly resourced.
He said the UK must face up to the “changing climate” and transition to “more clean energy”.
His comments came ahead of the appointment of Baroness Blake of Leeds as fire minister.
A spokesperson for the Ministry of Housing, Communities and Local Government said: “We’re making almost £1.95bn available for fire services across England, and investing £97m for the biggest upgrade of national resilience capabilities in nearly twenty years.
“We recognise that properties have been lost, firefighters have been hospitalised and people have been displaced, which is why we have also made available an emergency fund to support areas facing the greatest pressure.”
