I always thought the last BOAC/BA 707 was the one outside the Franklin Institute in Philadelphia which was scrapped in 1989. That was certainly the last one still in British Airways colours. See photo below.
However there may be one ex BOAC 707 that still exists....
In 1968 BOAC Boeing 707 G-ARWE was destroyed in a fire at Heathrow. BOAC needed a replacement aircraft. Later that year BOAC acquired a Boeing 707-39C registration G-AWHU which was an oddball aircraft originally on order to Saturn Airways. It was very different to the other BOAC 707s. One of the differences was the switches went up for on and down for off. I seem to remember the flight directors were different too,This was thought to be confusing so BOAC just trained 9 crews to fly it and those pilots and flight engineers flew only that aircraft until it was converted in the 1970's to the standard config.
It flew for BOAC / British Airways until May 1982 where it made its last flight from Cairo to Heathrow in the hands of Captain Hugh Dibley. After leaving British Airways it had 14 different registrations. That might be a record! I last came across it in Nairobi in the 1990s when it was flying for Phoenix Aviation and was parked next to my aircraft. I saw the pilots on the tarmac and they said it was an old BA one, they invited me to have a look so I walked up the their steps and had a look in the flight deck. I doubt you could do that these days without upsetting security!
Its last registration was 4L-GAS with Mach Avia who bought it in 2009 when it was 41 years old. It sounds like it made its last flight in 2013 when it landed at Fujairah in the UAE. In 2017 aged 49 it was still stored there. It may have been scrapped since or it may still be there but I have put out a request on the Middle East forum under the title "A Boeing 707 in Fujairah" as I was interested to know if it still exists.