Yeah, ice was used for food preservation. However, it's best to understand that it occupied a fairly marginal role, at best, in storing and preserving food for the vast majority of the population of medieval Europe. Salting, drying, fermenting and smoking were far more significant, having the advantages of being reliable, cheap and adaptable to the climate all over Europe. Ice, by contrast, was often (but not always) expensive and difficult to use effectively. Now, certainly you could bury food in the snow, in winter. And if you lived near a natural cave system, and rivers were icing over, you could go ahead and cut some blocks and store them in the cave, relying on the insulation of the stone to keep the ice from melting. But if we're going to talk mild regions like Southern England or Northern France, the overall usefulness of this method declines.

But, as mentioned, you could cut ice from frozen rivers and lakes. Under the right conditions, this ice could be surprisingly resistant to melting. Proper insulation, such as packing it in sawdust and straw, would allow ice to remain frozen-ish for the duration of a commercial transport (mostly this was used for overseas trips). In the case of your example, a journey from the south coast to London, it would only really take a few days to walk at most, and ice probably wouldn't be necessary (any meat-to-be could be driven in animal form and butchered on site). Even better, if you had a properly insulated structure - an ice house - you could store ice for months, with all the refrigeration benefits that entailed. Having a specific, engineered building for this purpose though was not cheap; this was the domain of the wealthy. There was also the problem of actually buying the ice you needed, most mild areas didn't have enough, and in later centuries it would start to be imported to Western Europe from Norway, and then increasingly New England, which was also something largely outside of the reach of most people. You would get your yearly shipment, and hope that your insulation kept it frozen through the year (which was often the case). Ultimately though, a lot of these developments post-date the middle ages. Certainly some ice houses existed (they've existed for a very long time indeed), but the kind of international trade networks that made ice a global commodity, and its use in food storage for the wealthy a common practice, wouldn't come until later.