When i got made redundant i looked into dog grooming the local college was doing a course but it was fully booked for upto 18months! A college course is the only way to go not an online course you need hands on experience, it maybe an idea to put your name down now.
Many many local groomers here offer 30day intensive courses i did look into that and they are in the region of £1200 and you basically work in their shop. The college option was much cheaper and they put you into work placements and they also had their own grooming school in the campus but alas the waiting list. The job centre 'may' help towards the cost of the local groomers course its at the persons discretion i enquired and they were only prepared to give me £200 towards the cost.
I ended up starting my own dog walking business because in all honesty i have NO artistic flair haha and i'd probably give a dog a mohican or similar.
I pay £15 a month for public liability insurance which would be all you would need too as my insurance is tailored specifically for animal workers such as us, such as if they have any accidents in your care, if it runs out the door into the road etc etc
Due to the petrol increase over here AGAIN its proving so expensive for my business right now and my car is going in for work done to in on Tuesday and i'm seriously considering buying a little 50cc Scooter to use from now until autumn i have a full driving licence so i can drive one regardless. I was wondering seeing as you don't drive would you consider that? the Compulsive bike training course is in the region of £80 for the one day and you could pick up a 2nd hand scooter for less than £400. The job centre WOULD help you with the cost of your provisional licence and the cost of the CBT course.
You could then become a mobile groomer my dad has one for his yorkshire terrier rat thing she carries everything in a rucksack and uses his dining table!!

this was what i originally wanted to do be mobile not confined to a shop.
My accounts are very easy i keep under the tax/vat banding per year for a sole trader, i mainly get paid in cash

i have a business account everything gets paid in and paid out from there and then i take my salary its easy. You should have a local chamber of commerce that would give you access to an accountant for upto 12months free to put you on the road so to speak.
Good luck i hope i've been of some help.
oh the online courses are pretty much a waste of money i know alot of dog walkers that take basic animal first aid online for instance i looked into it to see if it would aid my business and to be honest i wouldn't waste my money it was very poor. I've shown dogs for many years and i like to think i've got a good common sense about me and can do basic first aid without the need of a piece of paper which isn't worth the money.