Advice please:)

I'm sorry to read you're flying to the wrong city - best fly to Edinburgh

In another post you said you were flying into Edinburgh. Did plans change? Flying directly there would be easiest, but you could get an ongoing flight from London, or take the train. The train takes about five hours, but whether or not an ongoing flight would be quicker depends on when the ongoing flight was.

I know flying into Edinburgh is the easiest way. I am planning in using a buddy pass & the easiest/ surest way is to fly into London.

Here is what I did on a similar routing:

Fly to Heathrow arriving early morning (approvimately 90 minutes to get through immigration and get to the Tube station), take Tube to St Pancras/Kings Cross station (about £5 and about an hour travel time), get on a train to Edinburgh (£35 for a 1st class ticket advance purchase (drinks and the free snacks made the price worth it) and about 4 - 5 hours travel time), arrived in Edinburgh in time for dinner. This was a Sunday and everything was running on schedule. I still allowed a couple extra hours for the connection in case things were not on schedule.

You could also just fly from Heathrow to Edinburgh since you are already in the airport which would definitely be the quickest for travel time. 90 minutes £100 approximately.

"Quickest, easiest," since you're already at Heathrow, looks to be British Air to Edinburgh. We just did a trip where we had a flight to LHR and then decided to just continue on to Shannon. There were lots of people giving thumbs down on a trip with 2 separate bookings, but I was already ticketed by the time I got that bit of info. We had to transfer from Terminal 5 to Terminal 2. Other posters said a 4 hour window could still be tight, but we had plenty of time. But, we did not have a long wait in passport control line and we were on a direct flight from Seattle. We chose not to risk trying to see if we would be accepted through the "flight connection" system ( didn't want to double back if they wouldn't let us through), so just walked out of baggage claim and customs, followed the signs for Heathrow Express and took it (free) to Terminal 2. We checked back in for our new flight, went through security - pretty easy. And, it was on a Friday in late June.

As you're at the airport anyway, the easiest and quickest method is to use a regional connector flight to Edinburgh. I've done that with a code share flight on British Airways, and it worked well. Fortunately there was enough time between flights for me to enjoy a Full English Breakfast!

So, just to clarify, if you chose to take another flight from Heathrow to Edinburgh (since you will be right there) just understand that if you don't make that flight due to the first being late you will be out of luck. The two flights are not a "connection" they are two separate flights. You also must clear customs, so the timing might be difficult to figure. If you gave yourself a few hours then you should be fine, but then you are sitting for a few hours.

If you were flying BA or AA any checked bags would be transferred and you would only have to clear immigration. Within the Oneworld alliance historical policy was to rebook people even on 2 tickets but connection policies are in a bit of flux at the moment.