A couple of options spring to mind:
1. Beg, borrow, invest in a stand-alone reader - so you at least have that fall back possibility. I know that some people don't want the faff of needing a phone and a reader, as something extra to carry around. But needs must ....... I happen to find the Reader/Receiver option really useful from time to time
In principle your GP should be able to prescribe the reader. You are being provided with a medication (Libre 2) which is misbehaving and the one-off cost of a reader is small in relation to your care and wellbeing.
2. Consider switching to Dexcom One+, assuming your phone is compatible with that app. If it's not then the Dexcom One+ Receiver is a bit better than the Libre Reader. About the same cost (c. £50), but providing continuous readings in a smaller, lighter (so much less clumsy) device.
Dexcom One+ has the same tariff cost to the NHS as Libre 2+ and it is entirely in the gift of a GP to write the script. This was a major improvement from the spring revise to NICE Guidance Note (NG17), recognising that CGM users needed choice and that CGM could be (should be) prescribed by all UK GPs, not needing a Consultant to make a recommendation.
Three simple questions if I may,
@TraceyA: roughly how long have you been T1, which part of UK do you live in
and is your phone operating system, Android, ios or something else?