Flea infestations in rented properties are usually the result of previous tenants who had pets moving out. The fleas feed on the animal, breed, then drop off and lay there eggs in the carpet, usually around the edges. The eggs then hatch into small maggots which eventually turn into adult fleas which then need a host to feed on.
They find this host by heat. If the host animal has been removed then any human occupiers become targets.
You need a product which will cope with all 3 stages of the cycle.
Pertmethrin is the approved product for dealing with insect infestations and sachets of a suitable powder which is mixed with water and leaves a residual in the carpet and upholstery to deal with new hatchlings, is available from Craftex and Stapro.