the accountants are actually right, it used to be the case that you were given 3 months time since the start of your business to register it or yourself as self employed for tax purposes.
But they changed the rules so that you have to register it immediately when you start trading.
However the HMRC people informally are still going by the 3 month date for whatever reason.
I've been told by accounts that although you can register within the 3 month period, the rules state that you must register immediately or pay a fine or something. here's the thing, an accountant will tell you it's probably OK to register after a few months, but to cover his/her back in case of a lawsuit they'll tell you to register immediately. They can only tell you what the rules are. If they tell you otherwise they become liable for lawsuits and all sorts of other headaches
With regards to HMRC, I guess they will use their discretion and decide to fine you or not, the point is you CAN get fined, it's not an automatic fine. I guess it's up to the tax representative.
I do think they're mostly ignore that rule because it's a silly idea to force someone to register as self employed as soon as they start trading. Most people who aren't experienced in business will try something out on a whim, and do some casual work on the side. Forcing people to declare themselves self employed before they start trading is just more red tape, and will only serve to dissuade people from thinking about getting into business.
Although to be fair, our tax system is so dire that HMRC will have no clue you have a business on the side if you do it part time outside of your full time job.