I don't disagree at all. If you read what's been said carefully, I never argued they can't. I've only pointed out they haven't. And if you read my posts really carefully, you'll even notice I already pointed out what you're trying to say before you said it.My point is that there is no challenge. The reason the UK and France don’t build larger military grade engines is because they don’t have a need for them. They don’t make heavy weight fighters. Remember, the UK and France build engines that go on the largest wide body commercial planes. Up scaling the size of the engine is not a challenge for them. That alone should tell you that the absence of these engines does not exclude their technological capabilities from meeting the same or better levels.
I wrote high thrust in this class. EJ200 and M53 are the highest UK and French engines. SNECMA's M88 is a more sophisticated and modern engine compared to the M53 but it only outputs 50KN dry and 75KN afterburner. Compared this to WS-10A's 85KN dry and 130KN afterburner. These are old WS-10 figures from more than 10 years ago. More modern WS-10 variants are estimated to be similar or higher in thrust than AL-31FN series 3 and better.
So no I wouldn't put the UK and France in the high thrust league even though I'm sure they'd have no problems building one. They don't have the need to justify the costs but they have the industries and the technology for it. Here it's a case of not doing isn't the same as not being able to do. So far only China, US, and Russia have low bypass turbofans in the F110 class and above. Both Russia and China have used their AL-31 and WS-10 series to get thrust that approach F119 levels but have not fielded any engines of this class/generation or the even more powerful F135. EJ200 is 60KN - 90KN.
In any case, they haven't got any high thrust low bypass engines so it'll take them a while to build one even IF they can.