Mostly, I'm employed with contracts of employment.
Occasionally, perhaps once or twice or month - or even less often, I do some teaching for a large company. 1:1 language teaching with an employee but I'm paid (I set the rate) by the company. Company doesn't deduct NI and no tax comes off.
My thinking is that to stay within the law, I need to make a self-assessment? If so, and once tax is calculated, will I be able to pay it back with reasonably monthly payments - I don't have a lot of spare money each month.
If the income is less than £2,500 a year HMRC may let you pay the tax due through your PAYE code(s). Otherwise yes you will need to register for Self Assessment. Tax will only be due now on profits made up to 5 April 2012; if you cannot pay it all at once HMRC may agree a payment plan, or again to collect it through an adjustment to your PAYE code.
You say "contracts of employment" - people with more than one employment often find that due to various PAYE issues they have paid more (or, rarely, less) tax than they should have done, and sometimes more NI too. I'd actually recommend you look at all your P60s etc. for the past few years with an accountant to check - you might have a pleasant surprise!
Thank you very much - helpful reply. Can I ask HMRC directly about the possibility of paying any tax through PAYE?
I work part time and seasonally (term time only) for a couple of employers - this additional work doesn't happen very often but I am conscious of the need to be 'tax compliant' - it seems the right thing to be and, of course, the very large company is regularly audited.
"I work part time and seasonally (term time only) for a couple of employers"
In that case you are almost certainly paying either too little (if your tax code is 810L in both jobs) or too much (if it is just about anything else) tax - unless you already contact HMRC and have them produce a P800 and deal with any overpayment each year.
In these circumstances it is probably worthwhile completing a tax return each year; this will also enable you to claim employment related expenses, such as certain professional fees and travel expenses.
If you do want to ask HMRC to deal with the non-employment income through your tax code (although as your situation is not simple they may refuse and require you to move to SA anyway), look at [http://www.hmrc.gov.uk/incometax/non-paye-income.htm this information]] which has a contact link for HMRC.
just to add. even if you dont declare it the company you worked for may do so as part of their returns. This is what happened to me. I dint realise I owed it until I got a bill from hmrc for £895. They wanted it in one go but I appealed on the grounds that I dint know it was owed. They allowed me to pay back £50 a month which Im still paying!