Do you do a budget? Can you see what you will have to drop at likely £2K less a month income?
Approx £1K a month, surely - allowing for all the tax etc. that would have been taken out of that £20K.
Ideally, work is all about balance and how happy it leaves you in life. Many people don't get the choice to even consider that, but you're in the lucky minority who do. You seem to be dismissing all of those weekends together with the family as by-the-by, but they will be such a huge benefit. Taken to extremes, he could bring in over 55K doing a NMW job, if he worked 16 hours a day, 7 days a week - as some people do do - very few of them out of choice, though. Living to work rather than working to live.
Your time is important, and your own peace of mind, as well as your income. Management jobs don't always 'pay' more in purely monetary terms, but often in flexibility, respect, more freedom and - to turn things on their head - not having to do unpleasant/unsociable hours. Plus, as you say, this is the first step of the management ladder, which should bring further promotions with the same nicer number of hours, but with more money than he currently gets.
I say let him go for it with your blessing. If you're still left with nearly £100K income, it's much nicer to live a £100K lifestyle than to happen to get £120K, but in return have a £60K lifestyle, with a huge number of extra hours at nights/weekends and less respect, freedom and family time.