Once I complete my purchase - when will I get the deeds to my property?

Following registration of your ownership at HM Land Registry which  takes a few weeks, although the Land Registry does state that it will aim to complete all registrations within a period of 5 weeks. The time frame can fluctuate though depending on how busy the individual Land Registry is. Title to land is now electronically recorded so you will now receive a print out from the Land Registry evidencing registration in your name rather than a physical bundle of deeds. This is now what one would refer to as title deeds.