Not necessarily straight forward unfortunately!
Just because a house is empty, it doesn't mean it's an easy purchase. The only thing which is good is that you don't have one extra (at least) person in the chain. An empty house has all the same potential issues as a lived in house. You still want a good survey, good legal title and any work done on the property to have the correct paperwork in place etc etc.
As GU24Mum said, searches are just another part of the process. They may identify things which will need further enquiries and paperwork provided. Should there be any environmental issues flagged up (ground stability/flooding etc), you may be advised to seek further surveys/inspections.
The average time it takes to completion is around 8-10 weeks (freehold) and 10-12 weeks (leasehold) but this will vary greatly depending on what issues are uncovered and how quickly third parties respond to enquiries. So, you could be in before Christmas, but remember that the conveyancing didn't start when you received an offer for your house, but when the contracts were received by your buyer's solicitors and when the contracts were received by your solicitors from the vendor's solicitors.