Well spotted. I actually asked the article's author to address the concerns above, and they responded here:

https://atlaspragmatica.com/a-united-federal-britain/#commen...

Like you, they calculated the current take-home pay of this hypothetical person as £27,442 and, under the proposed UBI system, a take-home pay of £26,550. That's a one-off decrease of £892 which is about 2.5% of their gross salary.

For an imperfect comparison, Figure 5 here:

https://www.tuc.org.uk/research-analysis/reports/lessons-dec...

shows a similar real terms wage decrease in 2011, supposedly due to the political choice of austerity.

As another comparison, the Department for Work and Pensions estimated that 3.5% of their 2010-2011 budget was spent on administration:

https://www.whatdotheyknow.com/request/what_percentage_of_th...

Obviously replacing most benefits with a UBI won't remove all government administration costs, but it could lead to multiple society-improving outcomes (like improved health) which could reduce the over all tax level.