The LAA turned around my NPPL SLMG application same day and forwarded it to the CAA on Monday 12th. We're not far off the 10 working days now and as of this morning it doesn't look as if it's been processed (no money taken, and I had an initial class two medical and my old address was still on the CAA system). So I wouldn't cut it too fine!
I have an SSEA conversion booked for 7/8th, assuming all goes well I'll hand deliver my forms to Turweston that night. If not then I might have to wait and do it under EASA, at least there's a path for TMG.