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I struggled with this one for a while as my job would have most definitely been at risk - I don't handle money and don't sell any finance/insurance related products - but because the company is FSA regulated the above clause is in all our contracts, regardless of our role within the company.
Our company handbook, with regard to bankruptcy, states that we have to be 'of good repute' and 'honest' which I find offensive - the fact that I had petitioned for bankruptcy doesn't mean I am of ill-repute or dishonest!
In the end I decided to keep quiet; I was aware that the Official Receiver doesn't inform your employer of your bankruptcy and bankruptcy is no longer included in the public notices of local newspapers, as it once was (just the London Gazzette)
The only way your employer may find out could be as a result of your change in Income Tax code - a NIL code is applied for the remainder of the tax year in which you are declared bankrupt.
I purposely timed it so that I petitioned for BR mid-March and there
wasn't sufficient time, or any point in the Official Receiver requesting a NIL tax code as there were only 2-3 weeks of the financial year remaining - hence my tax code remained unchanged/no instruction to employer from HMRC to apply a NIL tax code.
I am NOT advising/suggesting that you do the same - I am merely sharing my experience as someone in a similar position to yourself.