a connection at terminal 5 with 1 hr 10 mins to make it

this isn't going to happen, right? (even assuming your first leg landed on time)

"I’ve got 3 hours on Wednesday and I’m seriously concerned I won’t make it"

Yes risky, but you're probably on a variety of watch lists, so it's different for you.

Is it two international flights, or international inbound with local outbound? 

People seem to be assuming the latter, but if it's the former (and I'm no expert on these things) you don't go through passport control, do you?

BA are helpful and efficient about this things ime. i've done international to international at terminal 5 in about 30 minutes when my first flight was delayed. someone will collect you from the door of the arriving plane, whisk you through a series of secret passageways, chucking you to the front of any queues along the way, and deposit you at the departure gate.

if your second flight is domestic they may be more relaxed about whether you make it or not, i guess.

 

if you are in biz and on a through ticket you should be off early and able to use fast track security (although last time I landed at T5 from the US it wasn’t open) which ime means you would be unlucky not to make it.