You can't even take shampoo to England these days, I doubt you can take your guns and leave them at the airport. The British dislike rifles in particular. Contact UK customs and ask is my only suggestion. BA may be able to tell you. Just get the answer in writing, otherwise you may be spending longer than you planned in the UK.
And you can't ship them unaccompanied without getting an export permit from the ATF and an import permit for the country you are going to. That's a major headache.
You may be able to fly to France, leave the guns with someone there, then do your UK visit without them. I think you can get guns into France with the proper papers.
