London Fire Brigade was called to the scene on Holloway Lane in West Drayton at about 4.30pm on Sunday and a 100-metre cordon was put in place.
The two-storey structure was burnt down and the cause of the fire was not initially known.
Station manager Sanjay Prasad said: "Firefighters are working very hard in difficult conditions to bring this incident under control.
"A number of cylinders are in the garden centre which is why a 300 metre hazard zone was set up as some cylinders can explode when exposed to heat.
"Quick-thinking firefighters were able to drag the majority of the cylinders away from the fire which prevented a possible explosion. Now firefighters are using covering jets to cool the remaining cylinders down.
"Fireworks are also being stored at the garden centre but again, firefighters are hosing the storage area down to ensure there is no chance they can catch alight.
"Most of the garden centre building has been damaged by the fire but crews have been able to contain the fire and prevent any further spread. Thankfully nobody has been injured in this fire."
Ansell said on Twitter: "Thanks for all your kind words and messages across social media. Just so surreal, know it's material but words can't explain the loss."
"Heart broken seeing 14 years of blood, sweat and guts go up in smoke. Thank you for all the messages. Thanks for touching base, thank god we are all okay and got out... thanks to the emergency services too."
Ansell managing director Paresh Raithatha took over the centre 14 years ago.
He said on Facebook: "We have been touched by all the kind words and support that you all have offered, from our family, friends, customers, suppliers, residents and our staff both new and old who have become part of our family. Thank you.
"Thank you to the firefighters and the police continue to provide all their support and monitor the garden centre (or what's left of it) to ensure the safety of the local residents.
"You all have given us the courage to move forward. We will hopefully see your smiles in the very near future and will keep you updated as much as we can so please keep in tune with our Facebook page.
"With some hope, we stay strong, we fight, we move forward."