Bowdeeni:
Ask the insurer if they will cover the Contents held in the container, if the container is taken away and entered into a secure storage companies compound/warehouse.
The problem any Insurer will have with the container in your garden, is that you will have access to it, so contents could be taken out of it and with all the works going on, the risk would be too high. Also the container could be broken into fairly easily and while they may be willing to cover for 30 days, the risk for a period of 10 weeks, is too much.
I have no recommendation for an Insurer who will offer cover, as I am not aware of a company who will provide this. You may therefore wish to reconsider the container and instead chose self storage at a secure site as an alternative.
In regard to the Insurance, I presume you have informed your Buildings Insurers and looked into who will be responsible for insuring the contracted works.
Huckster