We have all been far too sensible. What about the money no object, difficulties bedamned, last of the great Victorian eccentrics, completely batshit insane option?
The natural successor to the Lightning- the English Electric P.10, naming suggestion Longbow ? http://www.britmodeller.com/forums/index.php?/topic/234937581-english-electric-p10-sr2/
Say these words carefully. Wing burning- chamber ramjet biplane. Mach 2.5 sustained, 3+ dash. Twenty- five hundred mile radius. Huge equipment and weapon bays.
Extreme speed. Reconnaissance bomber role, originally, but adaptable as a heavy interceptor/ penetration fighter. Thrust deflector vanes in the wings and you could get the turn radius down to single digit miles at speed, or out- turn propeller biplanes at low speed.
Hell, if we're dreaming, why not dream big?
They did actually design a fighter version of the P10 called the P10E. It was shorter than the bomber version with length of v80ft and a span of 20ft. It had a 10ft long weapons bay carrying 2 missiles (allegedly AIR 2 Genies) with the crew being seated in tandem canopies. Rather that the 2 RB123 turbojets under the fuselage with the split-wing ramjets the P10E had 4 ramjets and 4 RB121 turbojets buried in the wing alternating with each other.
As a slightly more plausible all weather fighter you could use the English Electric P22. It was a fighter version of the P17 (Submission to GOR 339, eventually becoming TSR2) and had a radius of action of 1000nm. It could also loiter for 5 hours and had a higher climb rate than the Lightning! It could carry 10 Microcell rocket pods up to a total of 370 2 inch rockets or could carry 2 Blue Vesta IR missiles or like the P10E, 2 AIR2 Genies.