In the US you would want to Incorporate to maintain separation between your personal assets and your company assets. Location is immaterial as long as you set and maintain protocol.
Although this may be beneficial down the road, a C corp and even S corp may place undue legal, tax and accounting burdens on micro businesses. At least in my experience it was a serious pain.
I suggest an LLC, if anything. Personally I would run it as a proprietorship for a few years to see how it goes, then LLC.
Incorporating is not that expensive. My CPA and attorney showed me that the tax liabilities are minimal, the protection better. It is like E&O insurance, just another cost of doing business until you need the protection.
LLC filings are easy, inexpensive and offer some protection. For tax purposes they are extremely easy to deal with as opposed to C and S structures.
My S corporation cost me $100 to file as I recall, and my business adviser printed all the paperwork out for me so there was no costs for that. The administrative overhead for the company itself (not wages which is the same regardless of your company structure) is very low. At the end of the year, I do a P&L and produce a K-1 and add the net profit to my joint tax return.
Of course, this whole discussion is moot since the OP is in the UK.
I am talking about ongoing costs of a corporation.
You have to file monthly, quarterly, withhold social security, unemployment, taxed at corp level and at employee level, etc. etc.
All that has to be done by a pro in accounting, which I am not.
I rather spend my time imaging a 2TB drive through 1.1 USB to to 3.5" floppies, than work on my accounting book.
Your mileage may vary.
You should be OK as long as proper chain of custody documentation is observed and there is a secure (safe, locked, keyed closet, etc) area to hold evidence. As far as finding illegal content, you should contact your local authority and let them know of your operation and ask how they would like you to proceed if a situation occurs.
Since you would be working out of your normal residence, not a physically separate building, I recommend getting a signed document from the local law enforcement stating the nature of your business. Given the emotional nature of CP amongst the public you do not want to be open to accusations regarding such materials in your possession arising from your work.
/Greg