Hiding data by using a factory reset option does little to delete potentially sensitive information, suggest researchers.
Three separate investigations of Android's data deleting systems found it was possible to recover information.
In some cases, a reset just removed the list of where data was stored and deleted nothing else.
In particular, Tesco's Hudl tablet was found to have a flaw that let attackers get at data saved to onboard memory.
All the investigations used second-hand devices sold via auction sites such as eBay.
The BBC worked with security expert Ken Munro from security firm Pen Test Partners to get 10 Hudl tablets from the auction site and see how easy it was to recover information from them.
The Hudl was vulnerable, said Mr Munro, because of a known bug in the Rockchip processor at its heart.
All modern gadgets can be flipped into a "flash mode" so the onboard firmware can be updated and data written to the device.
"There's a flaw in the firmware, which allows you to read from it as well as write," he explained.
Using a freely available software tool, Mr Munro was able to easily read data from Hudl tablets to which the factory reset facility had been applied.
Getting access was the work of minutes but reading and analysing all the data typically took a couple of hours, he said.
Via this route Mr Munro was able to extract Pin codes to unlock devices as well as wi-fi keys, cookies and other browsing data that could be used to sign in to a website and masquerade oneself as the tablet's original owner.
In response, a Tesco spokesperson said: "Customers should always ensure all personal information is removed prior to giving away or selling any mobile device. To guarantee this, customers should use a data wipe program."
The spokesperson added that any tablets returned to Tesco would have all personal data wiped. They also recommended that people get further information about how to remove personal data from smartphones via the government's Get Safe Online website.
Google said anyone selling a used gadget should follow several steps to protect information.
"If you sell or dispose of your device, we recommend you enable encryption on your device and apply a factory reset beforehand," said a spokesman.
Data encryption systems have been available on Android for years, he added.
The next release of Android is expected to enable encryption by default. Currently it is up to owners to enable it for themselves.
While Hudl tablets were particularly vulnerable, other work has shown how straightforward it is to retrieve data from many Android devices.
The largest study was carried out by security company Avast, which recovered an "astonishing" amount of personal data from 20 second-hand Android phones.
The company recovered tens of thousands of images, including naked selfies as well as emails and text messages plus contact names and addresses.
"What people think is that when they hit erase or factory reset it's deleting the underlying source data but it's not," said Jude McColgan, head of mobile at Avast.
Independently, Marc Rogers, principal researcher at mobile security firm Lookout, has been cataloguing what happens to data saved on the main memory of Android phones and tablets when they are reset.
"There's an Android function to wipe data and most manufacturers are using that," he said.
"But all that does is remove the index of where data is and does not delete data at all."
A secure wipe would both remove that index and overwrite onboard memory with zeroes so it could not be recovered, he added.
"As a security professional it blows my mind that people do not do this to get rid of the data."
While it was not "completely straightforward" to recover data on those reset gadgets it was possible for a motivated attacker and the tools to do it were widely available, said Mr Rogers.
Motivation could come from the amount of cash stolen smartphones command, he explained.
Figures shared with Lookout by police forces suggest a street price for a smartphone with data on it can exceed $1,000 (£600).
The potential profit partly arises from the cache of personal, recoverable information people leave on these devices, Mr Rogers said.
In London, about 200 phones are stolen every day according to statistics from the Metropolitan police.
Recent work by computer forensics expert Jonathan Zdziarski suggests that data held on Apple's iPhones is also vulnerable to recovery.
Mr Zdziarski found that some undisclosed features in the iOS operating system bypass the data encryption system running on the device. This meant, he said, that if an iPhone was caught at the right time it becomes possible to extract information.
With effort, said Mr Zdziarski, using these undocumented features would let an attacker get at "privileged personal information that the device even protects from its own users from accessing".
In reaction, Apple has made changes to its mobile operating system that will be fully implemented in iOS 8. These should disable some aspects of the services he identified in order to limit their ability to export information.
Mr Zdziarski welcomed the "progress" Apple had made but said it needed to go further to fix the "significant security threat" faced.