Epic win

You're right about the volume of money, it sems quite high. Also, the HMRC don't usually call people. That sounds a bit suspect. Be careful about anyone calling up offering big fat sums of money and then asking for personal information (bank account details), no matter who they say they are. For reference, HMRC still write cheques and you can still request one rather than give out your bank details.

That's a very good point. They did know the name of my previous employer, as well as my current one.

Having said that, they asked me for my NI number, which means they may have been able to look me up on some system or other.

I will be extremely careful.

Thanks for the sage advice TSK.