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 IMPERIAL TYRES, UNIT 2264, DUNBEATH ROAD, ELGIN INDUSTRIAL ESTATE, SWINDON, SN2 8EA. That is the address the business gave the Environment Agency, and it is not necessarily where a collection vehicle is based.
A further 6 carriers are registered elsewhere in the SN postcode area.
Whoever you use in SWINDON, 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.