Just to follow up on this thread...
We've just returned home after a very enjoyable (albeit very hot) 3 nights away.
Broadway is a lovely village and we already plan to return, using Broadway as a base and exploring a little further afield.
Thanks again for the recommendations... In the end we ate, on the Friday night, outside at Russell's Fish and Chips as that was just what we fancied (as good a reason as any IMHO). Both Mrs T's cod and my haddock were excellent, as were the chips and the mushy peas. Table service outside very good too.
The other two evenings, we decided to avoid the crowds and fired up the BBQ instead of eating out:
The 'Broadway Deli' on the main street was excellent for supplies.
'Collins of Broadway' butchers, just off the high street, was a bit of a mixed bag. Bacon was good, their cuts of meat - the steaks etc also looked excellent, as did the rest of the 'deli' style products in the shop, but the the pork sausages and both the lamb burgers and beefburgers were underwhelming. The plain pork sausages appeared to focus on the 'plain' part of the description rather than the pork... texturally way too 'smooth' and too underseasoned for my preference. The burgers struggled to cope with the BBQ, quite 'dry' in texture and also underseasoned. The lamb ones particularly so.
Also on the high street, Otis and Belle Artisan bakery - very good indeed.
There is also a Co-Op, just around the corner from Russell's Fish and Chips, just in case you run out of chilled Vino Collapso.
For afternoon drinks sat outside overlooking the village green, watching the steady stream of Ferrari, Lamborghini, McLaren go past (and far the more common Aston-Martin, Porsche and Lotus too

) the Broadway Hotel was hard to beat. Good selection of drinks, (including 4x handpull beers if that's your thing - the 'Broadway Dark' porter was excellent even in the hot weather), and attentive staff that very much appeared to care about what they were doing despite it being very busy and very hot.