The team of researchers have teamed up with the Vodafone Foundation in the hopes of building a network of more than 100,000 UK smartphones to help process data while their owners are asleep.
Phone owners who want to lend their phones to the plan must download an app and donate some of their wifi or data plan, and make sure their handset is switched on and on charge for six hours per night.
According to Dr Kirill Veselkov, from the faculty of medicine at Imperial College, research into cancer is often slowed because of a lack of "access to supercomputing", and researchers hope mass use of mobile phones could hold the key to accessing the technology needed to further cancer research.
Kirill said: "Cancer research progress is slowed by a lack of access to supercomputing. It's needed to complete analysis - but it's limited and costly. This is a great example of a citizen science project - with members of the public directly involved."
Dr Veselkov and his team are searching for new combinations of existing drugs that can be tailored to cancer patients' individual needs.
He added to BBC News: "Let's say there are 10,000 drugs, with different combinations - that's a trillion possibilities. If you want to crunch these possibilities, it could take over 300 years. Harnessing the power of 100,000 phones, you can do the same in two or three months."
The research will take place via an app called Dreamlab, which phone owners will need to download if they wish to offer their phone's services. Data can be sent to the phone via wifi or using mobile data, with a cap of 500MB per month.
No data is taken from the device or any apps installed on it.
Analyst Ben Wood from CCS Insight said: "People forget that the processing capability of a modern high-end smartphone is as powerful as a computer from only a few years ago.
"It makes great sense to try and harness this resource, particularly when a phone is sitting doing nothing overnight other than being charged for the next day's use."