- If you send the visa application and documents on Monday after your biometrics (and purchase the priority service just before you send it), then you can probably expect it to get there by Tuesday 1st (if you overnight it using FedEx/UPS/DHL - don't use USPS because they are slow and you can't track the package).
- Then you have to wait for them to open the application which may take a couple of days (so between Tuesday 1st and Thursday 3rd, maybe?)... they usually send an confirmation email when they start processing it.
- After that, as long as your application is straightforward, it should be processed within 48 hours... so maybe by Friday 4th, possibly by Monday 7th if the weekend doesn't count in the processing time.
- Then they have to send it back to you which might take a couple of days, depending on when they send it, so possibly Wednesday 9th?
- Then you need to check the visa for errors and if there are any mistakes on it, you will have to contact the consulate to send it back and get it corrected (usually a short process... just takes a couple of days).
- The key thing is not to book any flights until you have your visa in your hand and have made sure it is correct... you don't want to lose the money for the flight if the application is delayed or it ends up being refused for some reason.
So, my guess is that if you get the visa to the consulate by Tuesday 1st, the earliest you might get it back is Friday 4th or Saturday 5th Feb, but it could be into the next week if they don't start processing it right away... it will probably depend on how many applications are ahead of yours in the line which they'll need to process before they start yours and also how long it takes for the visa to arrive at your house once it has been approved.
However, if you have anything that might make your application non-straightforward, such as any convictions or any previous UK immigration problems (refused visa, refused entry, overstay, illegal work in the UK etc.), that could add 2-3 weeks more onto the processing time, even if you pay for the priority processing.