Most insurance firms will charge about £25 (sometimes more) for a mid-year change in policy, which will likely negate any saving over that two week period. You have to make some legal arrangement at their normal home address, so I'd speak to your insurer to see what they can do and ask why the premium is so much higher.
To be honest, it's something on my list of things to check when I'm looking to move home, as significantly higher insurance can make a large impact on monthly/annual outgoings. You may want to check what your own premium may be rising to as well so you don't get another shock in a few months' time.
I would also check the details of your other address, especially the postcode to see whether it is correct. As Brompt says, sometimes moving not that far can make a large difference in premium due to the new one being a higher crime and/or higher risk (accidents - e.g. near to an accident blackspot [which you may not be aware of]) area.
I would also look at other insurers in case going via the first is an anomaly - you never know.
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