An exclusive licence may not need to be in writing and registered, for example where there is in fact an exclusive licence between a holding company and a subsidiary. However, this may prove more difficult to prove in evidence and some evidence of company policy might be required to satisfy HMRC as an alternative to a written licence.
Exclusivity must be across the whole territory of the UK but can be divided up in other ways, eg the exclusive licence to use a process might be separated from the exclusive right to sell the product of the process. To qualify, at least one aspect of the licenced rights must be granted exclusively.