I'm really sorry for your loss. KFDancer is right, you shouldn't let those guidelines on the gov.uk site stop you from travelling. I went through a similar experience to you just last year when I noticed those guidelines the night before taking a trip to France before my UK passport arrived. I made sure to check carefully with the UK border guards before I left and they said it was no problem. Indeed, it was no problem at all coming back in. They were happy that I was proud to be a UK citizen, and friendly. I also travelled to Italy during the same time period without any problem.
The United States has a law that forbids entering the US under a different passport than your US one, but I am fairly certain the UK does not.