Is it insane amounts, though?
It's private medical care, which means what you pay has to cover some part of all the things that are involved in providing that. Premises, specialist furniture and large equipment like benches, special fridges, locked cupboards, equipment drawers etc., all manufactured, maintained, cleaned and inspected to healthcare standards. The time and expertise of veterinary professionals who were selected from some of the most able applicants, who could've chosen almost any career they wanted, and who spent a great deal of time, money and effort training, need to continuously update their learning and who pay high fees for the training and for professional memberships, insurance and so on. The time and expertise of qualified, experienced nursing staff. All the support staff like admin and cleaning and practice management. The cost of the IT systems they need to use. The accommodation for animals while they're nursed in recovery. Specialist machinery for delivery of gases, for sterilisation, for weighing patients, God knows what else. Sterile or other medical and surgical kit — gloves, masks, aprons, syringes, shavers, scalpels, sutures, dressings, general clinical garb. Safe disposal of medical and other waste. That's before you even get onto the cost of medications, without the buying power of a behemoth like the NHS behind them. Medications are expensive because they have to be invented, tested, manufactured in whatever quantities required, regulated, monitored, stored in safe and sometimes secure conditions, and so on. Then unused ones have to be disposed of safely.
If you had a human with cystitis (maybe one who, like a cat, couldn't verbally communicate their needs, so it took a little longer to work out what was wrong, or the patient wasn't seen until objectively unwell) and you wanted to have them seen straight away by a team of adequately qualified people who could use their extensive training to work out what was wrong with them and exclude even more serious illness, diagnose them, treat them, offer advice to the carer, all in a safe environment using clean equipment and tested safe drugs where there was no unnecessary additional risk of medical harm, with nursing care if necessary, and with the practitioners involved insured against risk, etc. etc. then depending on the circumstances (maybe some out-of-hours care that demands higher remuneration, or emergency appointments, or aftercare requirements) I can easily imagine that topping £3k. Very easily.