I'm not British, but that site does seem pretty nice. I don't know anything about the history of it, but I highly doubt it was developed in house.
I don't think it's the case that the government is simply unable to do something like this, I just think they don't provide the right incentives like competitive pay and bonuses.
In the private sector, say in finance, if you're good and you work for the firm for awhile you could get promoted to managing director and make anywhere from a million to ten million in bonuses for the year. If you're a productive manager in government, you don't really get paid much more than anyone else.
The main benefit that government provides its employees is good benefits (healthcare, pensions) and job stability. It's unlikely that you will ever get fired unless for some very gross misconduct.
I think this incentive system attracts the wrong kind of people into government: those who just want a stable paycheck instead of those driven to produce value.
If we just raised government salaries or if the government gave out significant performance bonuses, the government would work a lot better and be much more efficient.