We have resolved the problems as follows although this doesnt address why the problem occurred in the first place:
We used MOm to monitor the increase in cpu usage by the SQL server agent over 5 minute intervals and noted that the increase started regularly at about 12:30 and would disappear at midnight. We have two jobs which are started just after midnight and run all day to monitor for updated jobs and database objects. Changing these jobs to run for 2 12 hour periods per day fixed the problem.