Meter Changers are not trained to a very high standard, so something out of the ordinary, like the cast iron cut out you have, is beyond their skill set.
It is the most dangerous installation to change, as it is common for them to fall apart when taken apart, due to age, and they are surrounded by metal, rather then bakelite/plastic. The meter changing wouldnt be a problem, it is taking the fuse out of the cut out that is the problem.
He/you should inform the Network Operator (Western Power/SSE/Energica etc) to come and change the cut out, the meter changer can then safely change the meter.