A key point to note is who you want to work for at the end of it.
easyJet and CAE are pretty hand in hand but they have also taken from L3 recently. Haven’t heard of them taking any FTE students.
As mentioned go for both EASA and U.K. licences if you can, this will keep the door open to go to Ryanair.
Of course there are more places to go than ezy/ryr but these are the two big frequent hirers and the most likely way to the RHS.
Also to be honest there’s no good/bad time to start training, you’re going to have Atleast an 18-24 month lead time and as the past few years have shown anything can happen.