So after a bit of work, I managed to get connect to this database:
jdbcDriver = 'com.microsoft.sqlserver.jdbc.SQLServerDriver';
serverName = 'Server';
databaseName = 'DBName';
instanceName = 'Instance';
url = ['jdbc:sqlserver://' serverName ';instanceName=' instanceName ';databaseName=' databaseName ';integratedSecurity=true;'];
conn = database(databaseName,'','',jdbcDriver,url);
So, as can be seen, I just made the URL itself, as the JDBC connection does have an instance property in it, however, MATLAB's database function doesn't so you have to manually do it.
It may be good if @MathWorks Support Team could add this functionality to the existing database code.
Thanks,
James