I assume that the company is run on a 'sole trader' basis (rather than as a limited company). If so, as a self-employed person, you get a £1000 per year trading allowance. So if your income from the self-employed activity doesn't exceed £1000 you don't need to submit a tax return. (I'm in that position myself).
If your income from the trading activity exceeds £1000 you're obliged to submit a tax return.
Anyone working as a contractor through an umbrella company is, for tax purposes, effectively an employee of that company. i.e. the umbrella company should deduct PAYE tax at source. So there's no need to submit a tax return, irrespective of the amount received through that company.