Referral to vets - appointment not for 6 days

I’m not asking for medical advice so I hope this is OK. My dog has been diagnosed with a large tumour in his spleen and kidney function of 500 . We were given the impression last night by my vet this was urgent and he referred us to a specialist.

However they have rung me today and said they cannot see him until next Tuesday - at which point I’m pretty sure his kidneys will have failed and he will he dead.

My question - will I be going against my vet by ringing around to see if other places can see him sooner or speaking to another vet and seeing if they can treat him instead.

I’m in England, UK