A few thoughts from a successful but now retired groomer. :)
I definitely wouldn't start mobile. You can't carry everything that you need with you, especially to a top floor flat! In the time that you're travelling, you can be trimming another dog and earning money. And bending over house baths is no good for your back longterm! :)
Train at a Grooming School rather than a college that offers a grooming course. In my experience you cannot compare the training. This is where I trained and then worked before starting my own parlour.
http://www.charney-kennels.co.uk/grooming.html Things have changed since I went there) many years have passed!) but I've still not found better training.
The time and money you spend is an investment in your future.
The work ethic that I was taught is trim to the breed standard and expect your clients to bring their dogs in every 6-8 weeks. With that in mind, after working for myself for 3 months I never had to advertise for the next 16 years and had a waiting list for clients waiting to a place. If you do once a year matted clip offs, then that's what you'll keep getting rather than owners who want their dogs to look good all the year round.