The registration is lower tier. Lower tier covers businesses that carry only their own waste, or specific exempt categories, and it does not expire in the way an upper tier registration does.
The address held on the register is UNIT 108 WIVELSDEN FARM, NORTH COMMON ROAD, NORTH COMMON ROAD, WIVELSFIELD GREEN, BN8 4EH. That is the address the business gave the Environment Agency, and it is not necessarily where a collection vehicle is based.
The BN8 district has 2 tyre-relevant registered carriers on the register, so there is more than one business to compare before you hand anything over.
A further 5 carriers are registered elsewhere in the BN postcode area.
Whoever you use in WIVELSFIELD GREEN, the duty of care under section 34 of the Environmental Protection Act 1990 stays with you: you need the carrier's registration number and a waste transfer note for every load that leaves your premises.