I flew from Houston to Jburg through London last year. It was a much more tedious process and nerve racking trip than the previous ones using Delta, Qatar or Emirates, but my Round Trip Ticket was under $1,000, EP status and systemwide upgrades got me upgraded the entire way so I rolled the dice.
Make sure you fly the same metal the entire way. Dont fly into or out of Heathrow on one airline, code-shared or operated by a partner and out on another airline. In London the code-share is considered an airline change and they won’t transfer them. They won’t let you collect the Firearms on a transit permit, and your layover definitely isn’t long enough for that. Save your firearms check-in paperwork. I had issues leaving JBurg and them telling me I couldn’t take my guns they weren’t approved but showed them this and it got fixed.