Have previous full distance walkers taken packed lunches out with them, or eaten out en route?
tomread, most of the days, we walked through some sort of town or village in which we could find something suitable to eat. That is, if we were, in fact, hungry -- many times, our full breakfast carried us through the majority of the day, and we carried a small amount of nuts, fruit, and/or nutrition bars to supplement our food intake. On longer days, we were usually able to find a cafe to eat something a bit more substantial.

However, there were a few stretches of the path (e.g., along Hatterall Hill, or in the midst of the Clwydian range) where we took our lunch with us -- either a packed lunch from the previous night's B&B, or a sandwich and crisps/fruit/etc. purchased at a village shop before entering the more-remote stretches of the path.

One thing about packed lunches offered by B&Bs -- Some are quite good; others aren't so good (either in quality and/or value-for-money). As our walk progressed, we increasingly tended to buy our own snack- or lunch-supplies in a village shop, rather than pay for a packed lunch at a B&B. If you do opt for a packed lunch, you might like to ask about the planned contents before you order it.