I used to be a self employed PA / Secretary about 10 years ago. It's a slog setting up as it can take you a long time to establish a stable client base. You really do have to go out knocking on office doors and leafleting around the businesses you target, which in my case were small businesses that might have not have the money or space to employ a FT PA.
TBH I never did get my business to the stage I would have liked and I got most my work through one-off contracts, which didn't give me a secure enough income. I could earn £500 one month, £20 the next and then nothing for a few weeks.
You do need to have a solid contract in place for your clients, detailing what you will provide, cost and, most importantly, your payment terms. I had one job that signed my contract then did not pay within my 30 days terms, insisting that they operate a 90 day turnaround. I could have taken them to the Small Claims Court but it would have taken longer than the 60 days left and eventually they paid up after 91 days
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If yoy have small children at home with you it will not be easy. Be prepared to work into the small hours to finish work. There's many a night I worked till 2 and 3am to complete a shedload of audio work because I had to stop work to pick kids up from school, make tea, sort bath and bedtimes etc, which is really frustrating when you know you have a deadline to meet.
My advice for start up would be to leaflet every small business in town; get yourself in the local paper with an "enerprising mum" story; visit business meetings, eg Chamber of Trade, and, most importantly, follow up all and any contacts you are given.
Remember to squirrel a quarter of all earnings away for tax and NI purposes, and remember to log all business mileage and keep receipts for everything as you can offset these against income on your tax return.
I did it for 6 years but went back to a PT job after the first year as I really needed a secure income and my business didn't give me that.
Feel free to pm me if you'd like to ask more, and good luck!