Ian Carter covers it a bit in his Red Kite book.
Dispersal of wing-tagged birds from reintroduced populations is high in Apr-May and the peak of spring 'passage' in the UK now is Apr/May whereas it was March prior to re-introductions and recovery of the Welsh population. Early spring (March) is more typical of 'natural' migration of red kites returning to breeding areas.
The conclusion was that some continental birds were involved but the majority are likely to be UK bred. Given it's based on dispersal rather than true migration, movements can be in any direction. Large numbers of kites are going to be far more noticeable in certain coastal areas without no or small kite breeding populations rather than Central England or Wales these days. Note a lot of these birds will be wandering immature/non-breeders - most kites don't breed till 2-3yrs old.
The origin of the released reintroduced birds is mixed so they had differing migration/dispersal tendencies, Spanish (dispersive), Swedish (most migratory), German (partial migrants), which will be all a bit melded together now.