Trace Hammond

Hi. I currently complete a tax return for work as a tutor. I usually record expenses as I consider I'm not trading; buying and selling. Expenses are way under £1000 I will be completing a return for some items I bought to resell which could attract a trading allowance. I also have work with employers/agencies as a teacher but this is not self employed work. Some of this is paid via an umbrella company, some directly from an employer. I will run the two businesses under different names. Do I have one trading allowance for multiple businesses or can I claim expenses for the tuition business and claim the trading allowance for the other business. Should I register the second business separately or do I do it all under one roof as a sole trader? Thanks.