Because everything is held electronically now at the Land Registry, you won't receive title deeds in the traditional sense upon completion.
You can expect the following:
A copy of any important post-completion documents
Fully signed and completed documents (ie. mortgage deed, transfer deed)
A copy of the updated title from the Land Registry confirming your ownership
The updated title can take anything from a couple of weeks to a few months, depending on the type of property and documents submitted to the Land Registry.
Ask your solicitor for a likely timeframe for receiving the updated title register from the Land Registry.