Grant, thanks for your reply.
I neglected to mention in the earlier post that the SQL Server log showed no error at all. There was simply the last valid entry of one log (a log backup being taken) then the next log started with the usual instance startup entries. I did however receive an agent alert email notification for a Severity 25 fatal error: The <InstanceName> service terminated unexpectedly.
For the windows logs:-
The security log showed the services for the new named instance being granted their various privileges, but no untoward errors at all.
The system log showed the various services of the new instance "entering the running state", 2 seconds later the next message showed the SQL Server Agent (Original) service entering the stopped state, following 1 sec later "The SQL Server (Original) service terminated unexpectedly. It has done this 2 time(s)." - this was the last message before I restarted the (Original) service. Once this service started it was followed immediately by "The SQL Server (New) service terminated unexpectedly. It has done this 1 time(s)."
The application log showed the installer going through its thing and then the new named instance starting up. Here the last service to start up was the Reporting Services followed by "The MSSQL$<Original> service terminated unexpectedly."
Essentially all I can see is that the new instance starts up and then the old one stops (and vice versa). Unfortunately there does not seem to be a lot to go on...