That certainly is a meaningful decrease in the EU's return rate - presumably also impacted by bandwidth for processing being strained recently - as is likely a contributor to the UK's drop.
"The EU's return rate was 38 %
in 2015, rising to 47 % in 2016, and
then falling to 36 % in 2018, 33 %
in 2019 and to 25 % in both 2020
and 2021." - taken from "Data on returns of irregular migrants - European Parliament" (I'd give a link but it goes straight to PDF download, which might not be welcomed - googling the phrase will take you right there, though).
The report flags that the drop to 25% in 2020 and 2021 was connected to control measures for the pandemic.
I don't think 2018/19s figures for the UK are a good point of reference (infact, all years post-referendum were likely impacted to some extent). One would expect countries to whom the UK is trying to deport asylum seekers to would reduce cooperation in an attempt to "run down the clock" until the effective date of leaving the EU.
- However - it is reasonable for flag that the largest drop (20% drop, from 59% to 39%) occurred in 2015, pre-referendum, and I don't think that can be reasonably attributed to a then-potential Brexit.
Ultimately though, its hard to say the extent and timing of reduced cooperation as a consequence of Brexit, but it does pollute the data.
Re. How many asylum applications have we actually completed the process for - i.e. refused asylum/ordered to leave the country, not pending appeal? you tell me, but obviously leaving EURODAC is a contributor to increased processing times.
Edit - that's @Clavinova