Doctors are hoping a new innovative technology will help make chemotherapy more effective and reduce the side-effects suffered.
The technology uses clusters of bubbles and liquid droplets to ensure the drugs used in treatment target tumours more successfully.
The drugs are injected near the site of the tumour and ultrasound is used to create high-frequency waves which "activate" the bubbles and droplets in a process called acoustic cluster therapy.
These waves cause them to grow larger within the tumour, stretching its walls.
This gives the chemotherapy drugs a bigger target to aim for.
It is hoped it will greatly increase the amount of medication which reaches the cancer cells, so if the trial is successful, it would potentially allow patients to be treated with lower doses of drugs, which would reduce the side-effects of chemotherapy.
The Institute of Cancer Research and The Royal Marsden NHS Foundation Trust are trialing the new system which is largely funded by Phoenix Solutions, which developed the technique, and the Research Council of Norway.
The aim of the clinical trial, which is still in its early stages, is to provide data on the effectiveness of the treatment as well as to establish its safety.
The therapy is being used to treat patients with tumours in the liver that have spread from the bowel or pancreas.
Eventually, the technique could be used to reduce the size of tumours before surgery - making them removable and potentially offering more patients a cure.
Karen Childs is the first patient to receive this innovative new treatment as part of a new clinical trial and called it an "exciting step".
Ms Childs, who was diagnosed with cancer in November 2013, said: "I'm not sure it's sunk in yet that I'm the very first patient in the world to be receiving this new treatment.
"This trial is an exciting step for the hospital and a huge step for patients like me.
"It really would make a big difference to patients' lives if side-effects could be reduced in the future using more targeted treatments like this.
"It's an incredible opportunity to be on this trial and the staff at the Royal Marsden have been amazing and very supportive."
Jeffrey Bamber, professor in physics applied to medicine, who led the work to develop and evaluate the technology at the ICR, said: "We're delighted that our work on innovative acoustic cluster therapy - which is designed to overcome barriers to drug delivery that tumours develop - has progressed to the point where the technology is now being assessed in patients for the first time.
"It's a very exciting 'door-opening' technology which concentrates more of the drug in the tumour.
"We expect eventually to be able to both treat tumours more effectively and reduce the rate and severity of side effects.
"In the long term, we hope this technology will be of particular benefit in difficult-to-treat tumours, such as those of the pancreas.
"It may also assist new types of treatments such as immunotherapy."
Professor Udai Banerji, deputy director of drug development at the ICR and Royal Marsden NHS Foundation Trust, added: "We're hopeful we can help open up a much-needed new option for patients with hard-to-treat advanced cancer.
"This trial is a real cross-team effort involving radiologists, physicists and nurses who all work together to provide the treatment and support the patient throughout the process."