All the mentioned UK auction houses will access good buyers if you have quality/rare coins and will show much interest very quickly . For middle level material, its better to offer a level of loyalty as a customer and 'shopping around' will inevitably mean exorbitant selling commissions. Sometimes it's best to lean towards one favourite auction house and stick to them.- I think you'll find they'll get to know you, lower their selling commissions and even help you find specific coins. Over the years I have purchased from all these auction houses, but when selling a longer term relationship is much better and I usually stick to the same house.