Britain did evaluate the F-15 but found the F-14 more suitable, being a two-seat interceptor from the ground up. You could have either Britain buy Iran's F-14s outright or have Canada buy them and order additional Tomcats to fulfill their requirement, bringing the unit price down enough to a point where Britain could afford them. Then maybe they can co develop the ASF-14 with the US for the RAF and FAA. QE's with Super Tomcats would be pretty cool.
Shameless plug here, but I did just most of that with Canadian Power. There, Iran's Tomcats were bought by Canada (the Canadian Caper stayed down long enough for the Tomcats to be delivered), and Canada's aerospace industry continually upgraded them, with a CF-14B version swapping out the TF30 engines for Pratt and Whitney units, and a CF-14C version being pretty close to the Attack Super Tomcat 21 proposal, that being because Grumman sold the proposal's designs and data to Bombardier after the US chose to not go for it. The Tomcat in Canada in that TL serves the Air Command from 1981 to 2014, and when Canada gets their big carrier in the 90s, it enters service with the Canadian Navy in 1997 and remained there into the 2020s.
I also had a much more powerful RN in that world - the POD is Trudeau attempting to shut up his opposition by buying the RCN a flagship in 1972, and that flagship is the former HMS Eagle. Eagle's first operational deployment for Canada is to back up our peacekeepers on Cyprus in 1975-76 and it proves itself there, so much so that Britain keeps the Ark Royal around a bit longer. It's decommissioned in 1981, but the Falklands War proves a utility for full-sized aircraft carriers, and Ark Royal is returned to service and recommissioned in 1986. Ark Royal sees service in the Gulf War and when Britain is involved in a mess in South Africa in 1992-93, and a confident Britain orders two full-size, angled-deck, 65,000-ton aircraft carriers to replace it, the first commissioning in 2003, and that one, along with the Canadian, Australian, New Zealander, South African and Singaporean Navies and air forces (and a little help from the Americans) take on the Indian Navy and Air Force after the Indian Air Force shoots down a Canadian transport plane and attacks HMAS Australia in the Indian Ocean in the summer of 2008. In that world, I debated Britain buying the Tomcat - it wouldn't fit on the Ark Royal or Eagle, but their replacements were designed with it in mind - but went with the Eurofighter instead, and a naval variant of the Tornado which sees use on both the British and Canadian carriers.