Thank you. It is possible to start working for someone else whilst still employed by one employer, although you need to check your contract to see if they have anything prohibiting this. But if you cannot work for them because they do not allow you to work from home and you are still officially sick and unable to do your job, you can do another job which you can do, such as because it allows you to work remotely. Just don’t claim sick pay from the old employer whilst working and receiving pay from the new one.
Regardless of what happened, if you were paid more than what you were entitled to at the time, then that is not money you can keep and you would be expected to repay it. So the employer is able to pursue you for that amount, even if it was their error that resulted in the payment. Of course, if you simply cannot afford to pay that in one lump sum and can prove it, they should accept a periodic payment over a reasonable period of time.
It is impossible to say whether employers usually take this to court or nit as it depends entirely on the employer and the people making these decisions. So whilst some employers will never consider going to court over this, others will not even think twice. I just can’t say which of these your employer is.
Whether they received sick certificates or not is not really an issue, as long as you were not fit for work and did not come I to do your job – if that was the case then you would only be entitled to sick pay, whatever that entitlement at work is, so if they overpaid you during that time you will have to repay it one way or another.
Does this answer your query?