Not all people will not be earning gettingon and taxation will be used to take back some of it from those with enough, earned or unearned, to really not need it.
Firstly it may be worth clarifying, that what we are talking about here is a 'partial' basic income. No one will be expected to live on it and, if it is taken up, some countries may wish to move to a 'full' basic income. But back to the 'partial' version we are talking about.
Let's say that the child citizen/basic income was set at £55/60. The various child benefits would disappear and so would some of the complex claiming. This, plus taxing it back off those at the top of the income table.
The adult one might be set at say £70/75. Again, no one would be claiming job seekers so this goes back in the pot. The amount of administration, cost of running job centres, etc., would also be put in the pot and again the tax system would work to take it back from anyone at the to of the tax system.
And let us say those reaching older age (67?) got a citizen/basic income was £155. This would mean that no basic state pension would be received. State pension is, in fact, paid from current NI contributions which is, in effect, a tax. It has never been a fund which mounted up before pensions were drawn. Again tax would be used at the top end and other savings would be made by simplifying the system.
That's my understanding of the basics. There are other areas where savings could be made and higher income achieved so either more tax paid into the exchequer or or less benefit paid giving more flexibility.