Officers said when they arrived at a station forecourt on Sunday night they could not refuel their police vehicle, meaning they could not effectively conduct rural patrols and were forced to resort to a bicycle to get around.
The Government has announced it will suspend competition law to help secure fuel deliveries to petrol stations across the country.
It follows days of long queues at station forecourts after fears of disruption to the supply chain sparked panic buying.
Business Secretary Kwasi Kwarteng said: "We have long-standing contingency plans in place to work with industry so that fuel supplies can be maintained and deliveries can still be made in the event of a serious disruption.
"While there has always been and continues to be plenty of fuel at refineries and terminals, we are aware that there have been some issues with supply chains. This is why we will enact the Downstream Oil Protocol to ensure industry can share vital information and work together more effectively to ensure disruption is minimised."
Ministers are also considering using the Army to help deliver fuel to help combat a chronic shortage of HGV drivers.
The Government has announced a temporary visa scheme that will see 5,000 HGV drivers allowed into the UK on three-month contracts up to Christmas Eve in an attempt to tackle fuel delivery difficulties.