Just remember when you're selling second hand things on eBay (i.e. stuff you have owned) that for the most part if you bought those items new and paid more than you sell them for then it won't be an issue with HRMC as if you're audited you can show a receipt for how much you originally paid for the item(s)
If you're making a loss on items - you wouldn't be much of a business person
. Even so, if you were doing this (buying and selling) on a regular basis, you would still need to register as a business. You would just file your end of year accounts and declare a loss.
There are some factors HMRC will take in to account and they will often make a decision based on their opinion, if you can't comprehensively counter it. So if you have not declared trading activity, you're not only going to have to pay the amount of tax HMRC have "guestimated", your going to pay a penalty too. As Doc said, you're guilty until you prove your innocence.
Some considerations are; if you are buying things specifically to sell them and not use them, improving them to increase their value, have a consistent pattern of buying and selling items.
If you buy something second hand, a car for example, and can prove that you have used it legitimately, then sell it at a later date (not the following week), that probably wouldn't be considered trading.
On the other hand if you were doing that with say a classic car, keeping it six months and trading it on for a higher price and repeating that a few times, then HMRC may decide that you are running a business.
Anyone who is a trading entity and is turning over more than £1k, is required to register with HMRC within 3 months of starting.