My original PPL application was sent off on Friday evening and I had my licence from the Board of Trade the following Tuesday. That was back before there were computers, fax machines or even national STD phones! But that was when government bodies issued licences and there were commensurate staffing levels.
Nowadays the CAA has to make a (small) profit and staffing levels have been reduced to manage a 10 working day turnaround time under normal circumstances. But when they're suddenly overwhelmed by 4000+ SOLI transfer applications, as well as having to work on 'hard' UK/EU exit contingencies, it's hardly surprising that SCC cannot provide a normal service.
SOLI transferred GA pilots will lose IR(R) privileges and that includes FI / FE. Revalidation of Part-FCL licences might not be possible in the UK if we leave EASA, as revalidation / renewal / assessment of competence / seminar requirements will need to be conducted either in an EASA MS or elsewhere if an FI / FE has been given approval to conduct training outside an EASA MS.....
Hopefully the UK/EU exit farce won't lead to the UK leaving EASA, perhaps just carrying on under the same terms as Iceland, Lichtenstein, Norway and Switzerland, which are all non-EU EASA MS.