Given your routing, I would bet the bag is still in LHR and didn't make the T4 to T1 transfer. This has happened to me on several occasions, and each time they have found the bag after a few days and delivered it to me. LHR baggage transfers are notoriously bad!

If I have the time, I seriously consider clearing immigration and collecting my bag at one terminal and lugging it to the other via HEX (free) and checking in again. If travelling in BA premium cabin and getting access to Fast Track for immigration, it is a fast and smooth exercise. Then having premium checkin at the other terminal makes that part of the exercise faster.

But the risk is running late for a connection if the inbound flight is late. Then again, if the connection time is tight I can almost guarantee the checked-through bags won't make it anyway.

last time through LHR my FRA-LHR flight (arrived T1) was delayed and I only just made my connection to LHR-MEL (departed T4). I make the transfer T1-T4 in less than 20 mins from touchdown. I knew then that there was obsolutely no chance my bags were on my MEL bound flight!