The oil giant said “a handful” sites have been hit by petrol and diesel supply problems.
There are around 1,200 BPO branded filling stations around the country.
It comes a week after BP told the Government that its ability to transport fuel from refineries to its network of forecourts was faltering.
BP's head of UK retail Hanna Hofer said it was important the Government understood the “urgency of the situation”, which she described as “bad, very bad”, according to a report by ITV News.
According to ITV News, Ms Hofer said BP had “two-thirds of normal forecourt stock levels required for smooth operations” and the level is “declining rapidly”.
BP does not employ HGV drivers directly, but outsources to independent haulier Hoyer.
The HGV sector has been struggling with recruitment in recent months with a combination of the Covid-19 pandemic and Brexit reducing the number of available drivers.
With test centres shut and many HGV drivers from the EU returning home during the pandemic, it has created a shortage of qualified drivers.
The issue has already hit supermarkets, with shelves half full and grocers forced to increase salaries and introduce signing on bonuses to fill gaps.
It has spread to waste collection services, with some councils cancelling bin collections as drivers have taken more lucrative jobs elsewhere.