There's a lot on the Tornado ADV decision in Battle Flight by Chris Gibson. Re the F-15, the factors were:
1. At the time the decision had to be made, there was a real doubt that F-15 production would continue past 1980, but the British Phantom replacement couldn't be afforded before 1985 due to the Tornado IDS program eating all the funds until then.
2. To meet RAF requirements, the F-15 would have to be substantially modified, with a fully-equipped rear cockpit for a WSO and probe-and-drogue refuelling.
3. The higher fuel consumption of the F-15 (and the F-14) relative to the Tornado would require a 30-40% increase in the RAF's tanker fleet, thus adding to their effective cost beyond the unit cost of the aircraft themselves.
4. Accepting the McDonnell Douglas proposal for European F-15 manufacture (which was only for the standard single-seater, by the way) would have effectively wiped out the UK's ability to design and manufacture advanced military aircraft. The UK aerospace industry employed some 200,000 people in 1973.