Thanks for your question which is now with the UK tax section of Just Answer
You state that you have £60K in the bank, how much profit do you think you have actually made in the last 6 years, do you think the £60K would cover the tax owed, any Class National Insurance and interest/penalties?
I think its admirable to make a full declaration, and it could be worth engaging an accountant to help you through the process, (as they can negotiate on your behalf) and certainly HMRC will think more kindly towards this situation, if you make a full disclosure, its just a matter of whether you have sufficient to pay what is owed (with all the charges) and also are in the position to pay of any balance that the £60K does not cover.
But HMRC are always open to offers of a payment plan, so lets see what sort of amount we have (as a ballpark figure) before worry sets in,
Could you also advise whether this was just income you made, or both you and your girlfriend (as a joint venture)