Yes, the Randox Tasso thing is really cool because you can do an at-home test still, easily on whatever day of your cycle you want to - and it's only about £45 which is way cheaper than any other private test I can find for a complete hormone panel... The results don't say anything about what sort of test it was (finger prick, venous, arm etc).
I've tested with a Tasso and then a couple weeks later a venous draw and the results are comparable (because I have to do venous for thyroid at the moment so I often take along a female hormone test to do as well, because I just pay for one draw however many vials they fill)... I have my Newson appointment tomorrow so if the results get questioned I'll let you know.
All I would say is that it can sometimes take the blood a while to get flowing into the tube after you stick it on your shoulder. Once I even was on the phone to them, telling them nothing was coming out... when it started coming out. So just be patient if it takes a while.