What is the common consensus on political consultancies as starting grad jobs? Is it worth it starting at a firm like fishburn hedges or fleishmann hillard to ride out the storm and then move to another 'proper' firm later?

These firms have nothing to do with management consultancy. They are PR/lobbying firms, the term 'consultancy' is a red herring.They might well be good places to work as a graduate, if you want to go into PR. If you subsequently want to move to MC, the fact that you have worked at one of these firms will be of no interest to recruiters.