Self Employed Earnings

The policy guidance states that one must be registered as self employed to count self employed earnings.

I did some work on the side, earning around £2k. At the time, I called HMRC and declared the income, who simply adjusted my tax code to account for tax/NI. Now I wish to include this 2k in the application.

I phoned HMRC asking about whether I should be self employed. I was told there was no point in my case because
a) If you earn under 2.5k in one year, that HMRC simply adjusts your tax code with your general employer to account for the tax
b) Just because you earn some money on the side, does not make you self employed. It depends on the nature of the work, and specifics of the service contract. You could register as self employed but that's only if you're a business with a regular income.

My concern is whether UKBA will accept this as earnings.
I have a service contract, invoice, bank statement and HMRC letter declaring the income. I don't have an accountant, obviously, as I don't run a business.
HMRC say that this isn't a case of being self employed - but I fear the UKBA might characterise it otherwise!?

Any advice? Thanks...