Try rewind vintage affairs London. They will buy birkins and Kelly's out right, and will sell other items in your behalf. you get more if you hold out and wait for the item to sell, but can take awhile.
I have used them and find them very professional.
There is also a seller based in Harrogate, can't remember name, but they buy birkins/Kellys outright, not sure about other H items. Search for birkins/kellys on eBay and you'll find them.
I have had same issue as you on eBay, when having a wardrobe clear out of high end items. They slap this restraint on all private sellers.
I try not to list/ relist too much stuff at once, and vary categories, ie not all bags or shoes at once.
Good luck with selling your items.