Anjou,
You started with saying that you needed a 30 - 36' boat. I think you got it right there, especially for single handing etc.
Since you are in the UK, you should look at the older Swedish boats made by Hallberg Rassy, Malo, Najad. They are not the lowest cost boats, but are closer to being a cruiser when they were made. As such will fit a live aboard needs better that the Plastic Fantastics of today.
You can visit my site to see a Malo 34 just to get an idea what is available closer to your length (not too big to handle).
Sailing Vessel "OLEANA" - Home and
h's Page - SeaKnots
Just type in the boats make into boats.com and you can see most that are for sale.
Good luc in your search.