No obligation to do anything from BA - sadly the outbound flight was already showing as 2hrs delayed when I was at LHR earlier, I would assume plane went tech just before departure based on that delay.

Flew PHX - LHR last night and was almost offloaded onto today's flight so glad that didn't happen, an offloading and then a 4hr delay wouldn't have gone down well.

I have bad news for you though,

BA0288 PHX - LHR is due to land at 17:11 tomorrow
BA0558 LHR - FCO is due to take off at 18:25 tomorrow

That is VERY tight, and only just over the MCT at LHR. I would suggest throwing yourself at the mercy of Flight Connections when you arrive and they may take pity on you (especially considering you might need a night at Heathrow). A painful lesson that only highlights the importance of booking flights through as a single PNR whenever possible !

Best of luck at Flight Connections tomorrow !

Ed