Dog grooming / pet-sitting
You will need space such as a spare room or a garage where you can set up the cleaning area with dryers and other kit so there will be some upfront costs. With pet sitting, you can either have pets at your home or go to other people's homes to look after them.
Don't forget about the legal side such as Pet First Aid courses and Public Liability Insurance which protects you in case there is injury to third party properties due to your negligence. Make sure any insurance you take out is accredited with the Association of British Insurers.