Customs going from SFO to Edinburgh

Passport control will be at London Heathrow for entry to the UK. If you are booked on one ticket through to Edinburgh, then the Airline should provide enough time, but don't dawdle. Do be aware that you will want to look for the lines for "Connecting Flights", that will keep you in the secure area (though you will likely go through Security to get to your gate), but it is much quicker still than leaving the secure zone and having to reenter.

Customs is a non-issue, just a walk through the "Nothing to Declare" door.

How much time should we allow for that process?

If you are buying one ticket that gets you from San Francisco to Edinburgh, the airline has figured out how much time is needed.

If you are buying separate tickets, then the common wisdom is 3 hrs minimum. If traveling at a time of year where weather is a factor, 4 hrs is the better idea

(though you will likely go through Security to get to your gate)

Yes, you will have to go through security as well. When you are connecting in the UK, you always have to go through security unless you arrived on a domestic flight. Unlike other European countries where you don't have to through security again if you arrived on a Schengen flight, and usually not if you arrived from a trusted country (such as other EU countries, Canada or the US).

Thanks all!
So, if we travel on one ticket from SFO to EDI with a 2 hr layover in LHR we should be fine.
Also, I assume we do not collect luggage until EDI?
Then go through passport check with luggage in EDI?

Thanks for all the input...

If you travel on one ticket you will be fine, the airline will not sell you a ticket if they think it's unreasonable.

You will go through immigration and security in London and customs in Edinburgh.