For yourself or a small community, this is possible, and certainly did happen in some places. The problem comes when you try to expand this on a larger scale to begin selling. The labour and cost of maintaining large fires simply becomes too taxing to make it worthwhile.

There were alternatives: if you were fortunate enough to live near a deposit of rock salt, you could mine it. This was reasonably dangerous though: salt mines are very dehydrating, and the combination of very dry air and physical exertion meant it had a high death toll.

A better method, and the most widely used until relatively recently, was to dig a large shallow flat pond, fill it with seawater and then let the water evaporate. This method is very old, and was likely inspired by people finding salt deposits on the shore. This has several advantages over boiling seawater: you don't need any fuel, and it's less labour intensive, as you can simply leave a salt pan for a few days, and return to harvest your salt. Large salt works using this method were reasonably common throughout England, including Nantwich and Northwich. Such salt pans would certainly have existed near Hastings.

If you want to learn more, Salt by Mark Kurlansky is probably one of the better commodity history books written, and very accessible.

Did people ever cook with saltwater?