A very similar thing happened to me. The figure involved was in excess of £6000 and I was contacted by the DWP regarding the overpayment as a result of being in receipt of an occupational pension. I sent them a copy of the letter I had written to them advising them i was going to receive the pension in October 2007, but I no longer had the certificate of posting to prove that I had sent the letter. The letter was stored on an old computer which I had to get going again to get a copy and I could prove when the letter was created but it still wasn't enough. I appealed and it was turned down. At that point I gave up and they are taking repayments from my ESA at the the rate of £36.05 per week. The rate at which they take the repayment depends on your overall income and savings. I wish you luck in taking them on.
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