There a few "amazing" deals out there for these weeks. During the pandemic (when many Brits could not travel) I picked up my 2-bed Platinum week for GBP 5500 (and at that time the GBP was struggling, so the conversion was favorable). Now, most weeks I see are in the GBP 8500-12,500 range. I used Worldwide Timeshare Hypermarket, which tends to cater to the UK. I would reach out to them on one of the weeks they have listed, let them know what you're looking for and your max budget. They can canvas the owners they have listings for and see if they can get close.
We love the Algarve and the resort is nice. It's not as plush as some of the other HGVC resorts, but the units are well cared for and the overall complex offers everything we need for a week.