If your pet is on long-term medication, try checking with your local 'supermarket' pharmacy such as Tesco to see if they can supply it. Our cat has a heart condition and is on permanent medicaction for it, the vets were charging £47 for a 3m supply, Boots wanted £40 but Tesco only charge us £25 for the same bottle.. as most vets don't like to stock medicactions they have to buy in specifically, so would normally pay more to order it in (except if it's an animal hospital such as the RVC), whereas a normal pharmacy will get discounts for the amount they buy... worth checking! I have to pay my vets £3 to write a private prescription, but it still works out much cheaper!
I'm guessing your cat is actually taking a human medication. Yes it is possible to get these on private prescription from pharmacies. The vast majority of human pharmacies do not stock veterinary medicines so would not be able to help the vast majority of cats who are long term medication. Also if you are insured it can be very difficult or nearly impossible to get these costs reimbursed.
Pharmacies now have the right to prescribe animal meds but they aren't allowed to dispense human stuff where there is an animal alternative. They don't routinely stock animal drugs and will likely have to order them in separately.
Vets aren't allowed to write prescriptions for human drugs unless there is no animal alternative.
Also vets are bound by the Cascade system. They are prevented from prescribing generic drugs and must always use the branded "for animal treatment only" stuff first EVEN if there is a cheaper generic available.