David Austin Roses head of cut flowers Ian Pierce said the firm's supply of cut roses from Kenya had not been halted but delivery drivers were taking precautions going from Mount Kenya to Nairobi airport.
He said: "They used to leave early [in the] morning. Now they are leaving at midnight and travelling through the night while people are off the streets."
Bedfordshire-based Chessum Plants owns production facilities in Kenya in a joint venture, which produces rose rootstocks for growing on in the UK.
Chessum sales director David White said its Kenyan nursery was still operating and supply was unaffected so far: "We were lucky to get most of our product in before Christmas and there is a natural break in supply for another three months." But he could foresee diesel shortages causing problems within the next few weeks.
CHA secretary Chris Wood said: "Nearly all internal travel is at a standstill and I am sure that this will be affecting the transfer of vegetables and flowers to the airport as well as affecting their ability to process goods even if they arrive at the airport packing stations."
He added: "We were planning a pavilion at Hortec Kenya on 12-14 March and had five or six potential exhibitors lined up.
"It now looks highly doubtful that the security situation will improve enough for us to go."