UK VAT legislation does not require you to register in that circumstance.
Your customer will need to use the Reverse Charge whether or not you are registered for VAT.
Thank you very much for your reply!
If I could only ask you one more question; my invoice contains the provision 'Reverse Charge' and does not contain any VAT information (either mine or the business that received my services). It additionally contains my business details and the business that is billed (name, address etc), the date, unique invoice number and of course the service provided as an 'item'. Is this wrong? If yes, what sort of information should there be mentioned on the invoice because I am pretty sure the invoice I issued is straighforward and abides by the requirements.
Thank you very much once again for taking your time to reply.