Basic, non-prescription pet health products — flea and worming treatments below the prescription threshold, wound care, basic supplements — are widely available in the UK at pet shop chains, supermarkets, and general pharmacies, with no special process required.
Prescription-only veterinary medicines (POM-V) are a different matter and legally require a vet's prescription, the same as human prescription medication would. Some items sit in a middle category (POM-VPS) that a registered pharmacist, suitably qualified person, or vet can supply without a full consultation, which covers a reasonable range of common parasite and worming treatments.
If your pet takes a specific prescription medication, bring enough for the full trip plus a reasonable buffer, along with a letter from your home vet. A UK vet can usually arrange an equivalent if genuinely needed, but it typically requires a consultation first, which takes time you may not have if you're relying on finding it last-minute.