The RSPCA is the only animal charity in England and Wales which operates a comprehensive rescue service round the clock with phones answered 24/7 and frontline staff available to go out at any time.
Summer always brings a surge of extra calls due to a combination of young wild animals getting into trouble; the fact that more people are outside and able to notice animal problems, and incidents due to the heat itself.
Extra phone-line staff are put in to manage this call peak, but there are limits on what is possible (there's no point spending so much money on taking calls that there's none left to pay staff to do the actual rescues).
In a lot of situations all an inspector would do would be to take the animal to the closest available vet for treatment, which is why we ask people finding animals in distress to do this if they have transport and are able to contain the animal safely. It takes much longer for an inspector to drive to their location and then to a vet than it would to take the animal direct to the vet.
The RSPCA has an agreement with the British Veterinary Association (BVA) which aims to ensure that stray animals and wildlife can receive at least basic treatment to relieve suffering. Vets agree to provide treatment for small wild mammals and birds brought to the practice in normal working hours and the RSPCA agrees to fund treatment of larger animals, treatment outside normal hours, and treatment of domestic stray animals (dogs are legally the responsibility of the local authority but the RSPCA will help if it is impossible to contact the LA).
You can read the current agreement in full on the BVA website and also some information on current negotiations to update the agreement.
For comparison, you might also like to take a look at the current arrangements between the BVA and the Scottish Society for the Prevention of Cruelty to Animals.
If you find an injured animal and you can safely transport it to a vet yourself, please phone the surgery in advance to check that they are open. All vets should have details of the number they need to call in order to get an RSPCA log number which will ensure that they are paid by the RSPCA for the treatment they provide.
And, please, don't listen to the people who say the fact that we ask the public to take animals directly to vets means you shouldn't donate to the RSPCA—donations are much more usefully spent on treating animals than on buying petrol.