Because I assumed the NHS online test ordering was closed, and after being unable to access any LFT kits for more than a fortnight, and also because I'm still waiting for the PCR I was supposed to be sent in January, I spent a happy half-hour trying to get through to 119 today. On the third attempt I got to speak to a real person who has proved to be incredibly helpful. He was able to order my PCR kit and said that if any of us are told they can't order on our behalf, we should ask for a priority test for vulnerable people which they can order through their admin service portal for PCR kits.
He also told me that under the NHS Living with Covid Guidelines, GP's are responsible for getting LFT's sent out but if we have no joy with the GP that the online test order line is still open for eligible people. Bearing in mind that I've been trying, without success, to order via the web for over a fortnight I wasn't expecting this but actually managed to place an order for LFT's about 30 minutes ago - Hurrah! Apparently, the reason that we haven't been able to get tests delivered wasn't due to a shortage of kits but because the number of delivery slots is limited so hopefully, it'll be better now that only eligible people can order.