Getting a prescription for stimulants is probably even harder than getting one for benzos here. Basically NICE guidelines describe your routes to meds. Helpfully they made a handy tool for you to see which mental disorders you would need before speaking to your NHS SSRI / Tricyclic loving psychiatrist.
(Interestingly, MAOI is now on there so for those struggling in the UK to get Nardil, printing this would be a way to eventually get it from a psych. You would need to go, SSRI -> other SSRI -> SNRI -> MAOI
So you can get an MAOI if you go down the route of social anxiety, you can get also get Pregabalin if you go down the route of GAD.
ADHD might be the only way to get stimulants here:
Refer adults with ADHD symptoms and moderate or severe impairment that have persisted from childhood and are not explained by other psychiatric diagnoses (although other psychiatric conditions may coexist) to a mental health specialist trained in the diagnosis and treatment of ADHD.
Refer adults who have been treated for ADHD in childhood and have symptoms suggestive of continuing ADHD associated with moderate or severe impairment to general adult psychiatric services
So pretty much, if you had ADHD as a child, could convince them it is impairing as an adult (might not be easy) you could get some form of stims (but not Adderall). If you had ADHD as a child and you weren't diagnosed, you are out of luck here I think.
Your psych might be open to Pregabalin or Nardil. It would be surprising if they went for anything else.