Marine litter is a global problem, in no small part caused by the persistent nature of plastics.
Responsibility is split. TTS have a cleaning team that include beaches in their remit. Department of Environment, mainly through the ECO-Active programme, promote and help organise beach cleans with various organisations (e.g. corporate, schools). Individuals also sign up to the Marine Conservation Society adopt a beach programme.
We are involved in reducing litter from fishing vessels by providing facilities on ashore.
Also I would hope all are interested in the care of our beaches and some responsibility falls to the general public to take their rubbish home after a day of the beach!
This is from the Department of the Environment [I especially like the last sentence]. This response suggests that any interest beyond that taken by TTS is going to be voluntary or aimed at fishing boats.
The Marine Conservation Society is the leading charitable organisation protecting the seas, shores and wildlife of the UK and, in this case, the Channel Islands. They coordinate and support voluntary beach monitoring and cleaning and produce usable data from the results. You can register as a volunteer or as an organiser on their website to help a local beach. I have registered as an organiser and intend to participate in the annual beach survey they hold. Learn more on their website mcsuk.org