Mr Davey said the council should use powers under government legislation to compulsorily purchase the land, near Tolworth roundabout, after the supermarket giant withdrew its plans for the third time yesterday.
Tesco bought the site, next to Charrington Bowl, in 2002.
Mr Davey said: “I think the council should think very seriously about compulsory-purchasing the site. I think that is the only solution, unless Tesco would put it on the market.
“It is time Tesco woke up. I think their decision [yesterday] shows they are on the run.
Mr Davey added: “We have been patient, we have waited for them to put these applications in and I’m afraid they haven’t listened to local people.
“We don’t have big pieces of land in many other parts in the borough left.
“We need some houses, we need some schools, we need community services. I’m not convinced we need a new supermarket.”
Tesco said yesterday it had scrapped its plans as they stand, and will now consider its options regarding the land.
Roberto Munoz, Tesco's head of corporate affairs for London, said the company will continue to consult on plans for the site which work "for the community".
The chain declined to comment on Mr Davey's suggestions.
Kingston Council officers had recommended the plans be refused at a development control meeting, now cancelled, which was set for Friday night.
The development would have meant the creation of 250 jobs, of which a third would have gone to people who had been unemployed for more than six months.
- GreanTea's Kingston and Esher members praised for Edinburgh Fringe success
- Kingston named as London's second-happiest borough
- One lane closed on A3 at Hook after crash causing delays back to Esher
- Line-up revealed: Ska, indie, reggae, bashment and dancehall to all feature at biggest Kingston Carnival yet
- New Malden school pays out to teacher fired after his 'sexualised' artist choice led pupil to Google explicit images