https://www.gov.uk/ukvi-premium-service-centres/use-the-super-premium-serviceAm I the last to learn about this? I had no idea such a thing existed... They come to you, take your biometrics and documents, and you get a decision within 24 hours ("usually")... all for the low, low price of £10,500 plus the visa fees. Wow! I'm gonna have to pass, though.
Anyway, the real reason for this topic:
I came across that service when I was confirming the additional fee (£75) for an out-of-hours appointment. My husband has been told he can start his new job on March 26th, but they won't be able to honour his holiday in the first full week of May booked at his old job. If he wants to keep that week off, he would have to wait to start 'til the next lot of new hires come in at some unknown date in the future,
after that week in May. He booked that week off so he'd be available to go to my in-person ILR appointment. It's not just a fun holiday for us! *grumble* (Though, admittedly, fun will be had when we're not sitting in the Cardiff Premium Center.)
So, now we're looking at a Saturday appointment in case he won't be able to take a day off because it's during his initial 15-week training period. We are really eager to book and pay before the fees go up in early April. So now our timings are going to be very close.
First Saturday I'm eligible for ILR is May 12th. So I can book and pay from March 31st. If I don't get that very first Saturday, we'll be spending a lot more money on my visa.

How hard is it to get a Saturday appointment? Are they in high demand? Are we going to be disappointed?