In theory the engine could carry on if used as a private aircraft however a lack of logs, time sat and possible AD's etc would tend steer one to overhauling it, but before you even touch that you need to ascertain the state of play with the airframe etc..
How long has it sat, indoors outdoors etc, you may have corrosion issues... Plus its a Robin with the probs listed above, it makes you wonder if the last owner got scared with a large bill coming up and retired it..
As said you really need a licenced engineer on board or part M Company who may accept help from you both on the labour intensive stuff to keep down your costs, they will be able to do a survey on the aircraft, check what's due AD and SB wise and let you know, may cost a couple of hundred, but if it saves you thousands of wasted pounds then its worth it.
And you will probably find the CAA will want to view the aircraft. The aircraft will have moved from a CAA to EASA C off A in the time it has sat, you will also need to figure into your budget things like Prop Overhaul ( gone are the days of on condition )
As for missing logs you will need to talk to the CAA and come up with an hours figure, you will need to satisfy all the ADs etc have been complied with...
To help you along you can get an idea of EASA Ad's by doing searches here for the Airframe, Engine, Prop....
EASA Airworthiness Directives Publishing Tool
For US AD's on the engine etc go to
Airworthiness Directives
Also the last owner may know where the books are, do a reg search here
GINFO Database Search | Aircraft Register | Operations and Safety
You can get the owners addresses from that.
With the date of the Annual the CAA might be able to tell you the company that did it, they may fill in some of the blanks and may even hold the books..
Good luck with it and I hope the two replies fill in a few blanks, but don't expect it to be cheap to do.