What were your results exactly? If you sat your GCSEs last year then it is too late to ask for mitigating circumstances if these have not already been applied.
Vet schools do not need to be lenient with people who have not met the grade requirements, as there are more than enough people that do. I have heard of people with relevant degrees being rejected for vet med because of their GCSE results; despite having a degree that requires much more knowledge than a GCSE does. Grade requirements are a very easy filter for them to apply to whittle down the applicant pool before they even look at personal statements, work experience documents etc. Ultimately it is at the discretion of the universities you apply to though, so I would encourage you to contact the admissions departments to ask if they would consider you. It is possible for your teachers to comment on how you were affected for your GCSE exams in your reference.
If you do not hear back with favourable responses then it's definitely not the end of the road as several universities (including RVC to my knowledge) accept GCSE resits.