Fly-tipping is the illegal deposit of waste in a place that does not have a licence to accept it instead of using an authorised method. This is an issue that affects many (estimated up to 67% of farmers) and costs a huge amount to deal with (estimated between £50 million and £150 million annually).
It is a serious offence that can carry hefty penalities of large fines, payment of costs, confiscation of the vehicle used to commit the offence and imprisonment. The perpetrators of such offences are therefore not just risking financial penalties but possibly even their freedom.
The bad news for you as a landowner is that if someone illegally dumps waste on your land it is your responsibility to dispose of it safely in the correct manner and bear the costs of doing so, albeit if you can identify the fly-tipper then you may be able to recover the costs from them.
Your local authority will only be responsible for clearing such waste from public land. Do not fall into the trap of moving the waste onto the roadside as this will mean that you yourself have committed the offence of fly-tipping. Do make sure that whoever you enlist to collect and dispose of the waste is an authorised waste carrier.