If it wasn't for the pandemic, Brexit and the whole issue of mutual recognition between UK CAA & EASA would be a lot clearer and I believe, a lot different. Most regulators are still working from home and it's going to take some time for the fog to lift and common sense to prevail. No doubt the HAS to be a meeting of minds to avoid chaos.
IMHO, the new, recently signed, Bilateral Agreement (BA) for mutual recognition of licenses and ratings with a simple conversion process, between EASA and the FAA (the latter being a third country in EASA speak) points the way to exactly how EASA will allow conversion from UK CAA (a third country now) to an EASA Part-FCL license in the future.
My current advice, which UK and European schools will likley advise against for obvious reason, is to use all the advantages of the FAA system (ease and cost) and then convert (later) to EASA using the BA. If you went to a school in the USA that also had UK approvals (if you are based in the UK) it is the icing on the cake! If the training process is well thought out, you could get your UK & FAA PPL's, FAA IR, get some good VFR and IFR time under you belt, sit the UK or EASA ATPL's when you are ready and the job market looks better and then rely on the BA to convert as needed. I estimate that this could all be done for less than £40,000 spread out over 2 years - surely this is affordable and a sensible approach? If I was starting again, it is certainly what I would do.
Rudestuff is right, stop agonising over EASA right now, go for a UK license if you are based in the UK and convert later when a job is likely in Europe.
If you want EASA and/or UK now, use the FAA BA to you're advantage, it will save time and money.