The landlord, Brunel University, is understood to have offered a lease which Wyevale decided was too short. The site may be developed.
Not far away in West Drayton, Ansell Garden Centre burnt down late last year - but there are plans to rebuild the centre and it continues to trade with a new structure planned for spring.
Malcolm Scott Consultants is working on plans for Ansell.
Two other nearby west London garden centres are also set to close.
Meanwhile, Jones Lang LaSalle (JLL) has applied to demolish Homebase in Swandon Way, Wandsworth, London and build in its place 343 flats, shops, offices.