Enough time to connect through Heathrow??

Connection time for terminal 1 to terminal 5 is 90 minutes without bag rechecking. If both flights are on a single ticket, BA will interline bags, which from your description seems to be the case. They won't on separate tickets outside the one world alliance (and not even always then). There are still some flights from EDI operated to LHR terminal 1 in August by bmi regional on behalf of BA. BA8041 arrives at 10:35 weekdays. This may be more convenient if US is happy and able to switch you onto it. Connection time T1-T1 is given as 60 mins, but I've been through into the lounge area in much less than that.

To clarify what Marco said, the connection time of 90 minutes isn't how long it takes, but the time they say you should be able to make a connection in. Since the time you have is more than 90 minutes, you should be fine if you arrive on time and don't mess around getting to the other terminal. Arriving on a later flight just because it's in the same terminal would make me even more nervous than what you have now.

The times I mention above are the minimum connection times listed by by the airport for legal connections. If arriving at T1 domestically in practice I have been back in the departure lounge for a same terminal connection within as few as 10 minutes. This is because you don't have to clear any further security or bag checks under normal conditions as you are still 'security clean' (the same is the case for T5-T5). If coming in to T5 you need to get on a bus, and when reaching T1 have your hand luggage checked, and go through security screening. Much lengthier process, because you are 'security dirty', having mixed with international connecting passengers. I know what my choice would be but realise it might not be everyone's.

I guess it's the question of whether or not BA could or would switch you (and what that might cost) vs. the potential time savings.

Since the flight change appears to have originated from US further changes may be possible, but this isn't certain of course. Possibly when the OP made the original reservation it may have been a bmi connecting flight dating back to it being in the star alliance before it was sold to BA.

The original flight was a bmi flight from Edinburgh to Manchester then US airways to Philadelphia. They first changed the times on this and the US airways agent said they no longer had a code sharing agreement with bmi but with her supervisor had got it all settled. One week later I get an email with the latest changes (I'm sure they switched to BA because of of the dropped agreement).
So, ya'll saying as long as I hustle through the airport, pick up my bag, take a bus to terminal 1, recheck my bag and get my boarding passes for the remainder of my journey, go through security and (hopefully) have time to run to the bathroom, I should make it???

You should be OK, yes, but I would print my boarding passes for the second leg before getting on the first plane (internet cafe, your hotel). I think your bag will be checked through, but they can verify that in Edinburgh.

... So, ya'll saying as long as I hustle through the airport, pick up my bag ... If it is a single ticket you should be able to check the bags through and do the connection airside (follow connection signs). US and BA do interline. You do always have the option of doing it landside, but I can't think of any benefit of doing this. My suspicion is that US Airways agents are unaware that currently BA flights from Edinburgh arrive at two different terminals. You should however have sufficient time to make the connection however you do it.

Thanks to both of you for your help. If anything, it will be an adventure :)