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Even more comlicated by the late OR346 types having a 36 inche dish, able to detect a target at 70nm, but not stating what radar that is.
While AW406 required detection of a "Canberra sized aircraft" at 60nm, and this may relate to a 30inch Aspinal CW set, projected for earliest service in 1970/71.

Worse still the AI.20 Green Willow x-band set used on the Swift F7 was supposed to detect a Hunter sized aircraft at 10nm, but this is a substantialy smaller dish!

AI.23 in the Lightning was a 24inch dish = 3.142 sqft
AI.18 was a 28 inch dish = 4.276 sqft

So quite a difference in dish area.

However the Supersonic Scimitar Type 576 had a AI.23 set only able to detect a "warship" at 60nm!

Marevelous site concering EKCO here. Including the AI.20 set, reading about its reincarnation as Red Steer, it might well have been the same 18 inch dish, and this would mate with likely dish size of the Saro P177 fighter.

http://www.ekco-radar.co.uk/poole/ai20.php

Curiously the later improved Red Steer set on the updated low level Vulcan raised dish size to 24 inches but the site is quiet it seems on the increases in range this brought about.

Transmission power is only half the equation, dish size equates to the ability to 'scoop up' returning radar reflections.
Power laws also relate to the distance, twice the distance say 40nm would produce a fourth the return signature at least, way too faint for the AI.18 to discriminate from scatter.
So logic suggests you'd need four times the sensitivity or reception area to get the same signal from a target twice the distance....?
Ergo that would require a dish the size of 56 inches.
SO the 40 inch dish must be matched with higher power in the beam surely? Or else perhaps it was only 25% more range for the F155T winner (Delta III), at 25nm?
That would rather suggest something about the expected performance of the Red Hebe AAM the improved AI.18 was supposed to guide.

And yet the yanks where well on the way to producing 40 inch dish sets with far higher detection ranges.

Damn should've remember that one of course, the signal has to go both ways.
Still with sufficient increased power and a larger dish higher detection ranges must've been possible.

Interesting asside, the AN/ASG-18 early efforts by Hughes was only able to detect a B52 sized aircraft at 40nm, took a lot of effort and some time before they got the system upto 130nm and at this time Hughes is one, if not the best, at this sort of thing.