The HMRC has a dedicated self-help/learning site that is helpful here:
It's important to tell HMRC that you are self-employed as soon as
If you don't, you may have to pay a penalty.
You don't want to pay more to HMRC than you have to as it is a waste
of your money.
Your business has started when you start to advertise or you have a
customer to buy your goods or services.
It is at this point that your business is 'trading'. You cannot
register before you start trading.
For example, if you advertise your business in the local newspaper on
15 January but do not get your first customer until 29 March; in this
case, you have been trading since 15 January.
You must tell HMRC within six months of the end of the tax year in
which you start self-employment.
You must therefore register by 5 October.
But it's best to register well before this so that you do not forget
to do so.
The HMRC also has a YouTube channel with help videos, and "Am I Trading or Not?" might be of particular interest to you.
Most of the registration is based around the concept of starting to work with the intent to make a profit. By the letter of law and regulations, you should register within six months of the end of the tax year you started to avoid any potential penalty.
However note that the situation is different based upon your intent. If you begin making/putting up videos online as a hobby with the hope that you can make something to help you defray the basic costs involved, and the total amount you make is relatively small (say, less than 500 pounds), you will not be classified as "trading" and likely have no need to register with HMRC.
As soon as you begin to get in regular payments, maybe a single payment of a significant size, or multiple payments for a similar service/item, you are vastly more likely to need to register.
From my reading you would likely be safe to begin putting up videos without registration, but if you begin spending a large portion of your time over an extended period (multiple months) and/or begin getting payments of any notable size then you should likely register with the appropriate services (HMRC, etc).
As is the case in both the USA and UK, simple registration is pretty cheap and the costs of little/no income are usually pretty minor.
Also note that the HMRC trading and self-employment regulations are unusual compared to many US laws/institutions, in that you are explicitly permitted to begin doing something and only register later. So if you start doing videos for an entire tax year + 5 months and make nothing significant, you'd seemingly be fine to never register at all.