Whilst this is very admirable and kind - you're running a business, and with the economy the way it is, if you want to last you have to raise your prices. There is an in-between, somewhere more than undervaluing your business and its services to such a degree, and less than charging over the odds like Vets Now.
Does your practice employ other vets that perform OOH duties? I'm assuming their salary reflects that, if they're paid fairly? So, you should not be charging absolutely 'nothing' for an OOH service. I'm confused why you aren't already charging extra, if even this was a nominal amount compared to the Vets Now that you reference.
I've not seen a consultation charge of £15, ever in my life, and let's just say that I'm older than 30. I've used chains, I've used independent practices, alike. Independent do tend to be cheaper, but again, I've never paid £15 for a consult in my entire life, it's always, always been more.
Again, it's very admirable that you are trying to keep costs low for the customer, and I assume you have a very large customer base as a result. However, the brutal fact is that this is why your business is failing - not because of NMW cost increase and NI. You don't have to be Vets Now - you just have to change with the times and increase the fee for your services.