Solved this by closing Visual Studio 2013 and locating the path of the localdb which was WebApplication1\App_Data, there were two files aspnet-WebApplication1-20140430012043.mdf and aspnet-WebApplication1-20140430012043_log.ldf residing in that folder.
I modified the security permissions of WebApplication1\App_Data so that SQL Server 2012 would have no issues connecting to it.
I then opened Microsoft SQL Server Management Studio and proceeded to attach the database, once the database was attached to the instance, I backed the database up. Next I dropped the database and carried out a restore, this time renaming the database as per the project and relocating the mdf and ldf files.
I then opened my project in Visual Studio 2013 and modified the Web.config from:
<connectionStrings>
<add name="DefaultConnection" connectionString="Data Source=(LocalDb)\v11.0;AttachDbFilename=|DataDirectory|\aspnet-WebApplication1-20140430012043.mdf;Initial Catalog=aspnet-WebApplication1-20140430012043;Integrated Security=True"
providerName="System.Data.SqlClient" />
</connectionStrings>
to:
<connectionStrings>
<add name="DefaultConnection" connectionString="Data Source=MYSERVER;Initial Catalog=WebApplication1;Integrated Security=True" providerName="System.Data.SqlClient" />
Ran the project and all is well.