Car insurance for person coming from Poland with EU driving licence

If your brother-in-law has a EU driving licence and he's not banned from driving, then that's fine. However he needs to be insured to drive your car. If his Polish car insurance policy allows him to drive a car outside Poland, that is, in the UK, then there's no problem but if that's not the case, then he would need to get additional cover before he can drive your car. You can look into temporary car insurance for him or he can ask his existing insurer if they can extend his current insurance policy to drive in England for a few days.