It's not the documentation that's in your hands that's important, it's what's on the Land Registry's computer. (You might get nothing more than a letter from your solicitor, confirming that the transfer has taken place).
It will cost you just £3 to get a copy of the title register, showing you who currently owns the property. (It's an extremely simple thing to do. I did it myself, in relation to a neighbouring property, recently):
https://search-property-information.service.gov.uk/
It may be that the transfer has already been completed.
(Note that the downloaded title register can't be used as proof of ownership in a court of law, or anywhere else a formal document is required. You ned to order to order an official copy for such a purpose; it takes less than a week:
https://www.gov.uk/government/publications/official-copies-of-register-or-plan-registration-oc1 )