In the UK, if I am involved in an accident that is not my fault will I lose my No Claims Discount?
If the No Claims Discount is protected, can I still move to another insurer?
I don't know about the UK (however it should be the same), but in Australia if the accident is not your fault and you are able to prove this (i.e. signed statement from other party, police report, independent witnesses) you should not lose your NCD. You should double check this with your insurer.
If your NCD is protected with your current insurer then even if you are at fault in an accident you should not lose your level of NCD. If you move to another insurer it would depend on the new insurer whether you retain your NCD protection, and it is something you need to check and/or negotiate with them.