Small numbers of sales, a low volume, a small income, thats a private seller.

Inherited items, thats much different. What you seem to be saying is that you have inherited a load of items that may be worth some money. Enough to be selling it on eBay and paying their fees. The schedule received from your lawyer of possessions and the value you declared to HMRC for the purposes of inheritance tax (a legal requirement) will indicate what level of tax, if any, you paid on the transfer of those goods. 

If you then decide to sell them at a business rate then you must declare the income. But you can put the schedule cost as your cost of sales so that you dont double pay tax. If HMRC came chapping, you could produce the schedule as evidence. 

Obviously if you then sell more than the schedule value, then you have an income to declare as you have made more money than you declared to HMRC. 

Of course HMRC are not likely to be interested in someone that has a feedback of  48 items in 12 months with a total of 759. But the seller who has a positive feedback of 58885 and 2554 this year is very obviously a business for tax purposes and I would say is ripe for an early inspection. If they have declared a large value for inheritance tax then they will be fine. The cost of the storage unit can obviously be deducted from business income as can all eBay and postage costs. It may be in the end that no tax is due, but I would say with those kind of numbers the HMRC are going to be looking at the last 7 years in due course.