The post office guidance is here:
http://www.royalmail.com/parcel-desp...1st-class-mail

BUT - (note the big but) it depends on when it is going to be posted. Your Amazon order will usually give you an estimated dispatch date, then you get an email telling you when it has been dispatched. I usually find that for SIM's they arrive the next day after dispatch. You can go into your Amazon account and look at orders awaiting dispatch and see where you are.

I regularly order SIM's (for iPad data), and I find it is a very quick service - depending on who your 3rd party supplier is. If it goes in the post within 24hrs of your order you get it after 48 hrs. If they take five days to post it, you get it on the sixth day unless that is Sunday, when it arrives on the seventh day. If posted second class, add up to two more days.