"This idea of spending £5 this year rather than £50 and it being a better option even if that means it costs you £5000 extra over the next 3yr I cannot rationalise"
If you had a stable, known future income and you had control over your own saving and future purchasing ability, then yes I agree, that sort of decision making is irrational*. But that's not how MOD or government budgeting operates.
For MOD budgeting, spending £5 instead of £50 purely means that you've saved £45 today - and that's the good news headline that your budget holder has been ordering you to come up with because that £45 is needed right now for some immediate other thing. An analogy is if in your own household, you spend £5 instead of £50, that means you now have £45 to spend on food for the week so you can stay alive. (a better analogy might be that you £45 to pay for the £40 worth of food you got on credit last week to live on. This week's food is a different crisis).
The idea that by doing so (ie staying alive) you've committed to additional spending in future years is a problem kicked down the road, kicked out of sight and out of mind. The thing that you might have to spend £5000 on now might be scrapped, or made cheaper by some magic creative accounting or it's just one of many things you want but can't afford anyway. And all the while you are living hand to mouth anyway, as you go cap in hand every few months to the keeper of the magic money tree (which is neither a tree, magic, nor actually containing any money).
That's how MOD "budgeting" seems to operate.
*Imagine if you said to your boss that you were putting aside £100/month to save up for a new car in three years, and their reaction was to dock your pay by £100/month because you are clearly don't need that £100. Or, you told your boss you were putting aside £100/month for a rainy day, and your boss instead fired you for financial rule breaking and sued you for all your rainy savings to be returned. That's government budgeting!