There are lots of ways you can get blood tests done without involving the NHS, but of course they all cost money.
I have personally used Blue Horizon Medicals, and also Genova Diagnostics UK. Other companies are available...
Blue Horizon have several websites :
This one is for finger prick samples which you can do at home, and then just send off in the post. Obviously there are limits as to which tests can be done with such small amounts of blood. I've never tried this particular site, but I've read of plenty of people who have and found it perfectly acceptable.
This one is for full blood testing (i.e. a full blood sample in a tube is required). This site and the testing is done in conjunction with Spire Hospitals. The phlebotomy service is included in the price, and the sample is just left at the Spire Hospital for processing.
Similar to number 2 except it is done in conjunction with Nuffield Hospitals.
This is for people who can arrange their own phlebotomy and are happy to send blood samples through the post.
Genova Diagnostics UK have one site :
They do blood and saliva testing. People can either use the phlebotomy service suggested by Genova (in London and Surrey) - phone up to confirm it is available and open first :
or they can make their own arrangements to have blood drawn.
Samples are usually sent back through the post using guaranteed next day delivery, or they are sent via courier, again for next day delivery. All instructions, kit and packaging required is sent to the patient when the order is made. Payment details are only given when the samples are returned.
For Genova, they require the name of a practitioner or doctor to put on their records. If you use the name "Thyroid UK" that is acceptable.
I can't remember if the requirement is the same for Blue Horizon, sorry.
More info can be found here :