This one isn't easy, but as I understand it:
Have you ever held an SEP class rating on your IAA licence? If you SOLI'd to the IAA, did you hold an SEP on the previous licence? It would be useful to know whether it would be initial issue of an SEP that you've never held before (common with integrated courses) or a renewal of a rating you held at some point.
If it's a renewal and the SEP expired less than 3 years ago, you can do training as required with an instructor and then test with an examiner to get the SEP back. An assessment of no training required is acceptable and doesn't need an ATO/DTO. This will be the simplest method. FCL.740 (b)(2)(ii).
If you haven't ever held an SEP, or it's over 3 years, you'll need an EASA ATO/DTO. There are a few in the UK, or you could travel to the EU as Covid rules are relaxed.
As things stand right now, the CAA website states the end date for using an FAA declaration is 20/6/2021. It may change in the meantime if a BASA is negotiated or the derogation is extended. ORS 4 No 1380 is the latest position on this.
Regarding the two year validity, I asked two experienced examiners (FE CPL/IRE) whose advice I trust and they said you can use a rating until 31/12/2022, but not a certificate. So, you're ok to use your SEP/MEP/IR even after revalidation but not an FI/FE/medical. That position is backed up in part by IFEA and published here:
https://ifea.uk/news.
Edited: We don't know for sure what will be required beyond 31/12/2022, as things stand and if there's no further deal you will need a UK licence to fly G-reg.
I would love to be able to back up the "you can use a rating" advice but I cannot find it written in legislation. I'm not a member of IFEA or I'd ask this question there. Any other FEs with a different perspective?
I'm sorry that's not as definitive an answer as I'd like to give, but hopefully it's a move in the right direction..