You do not tell us what time of year you will be visiting the Cotswolds area and what activities you will doing such as outdoor walking or visiting places of history.
Lets assume you will be over here this summer.
1. Restaurants
Luncheon - bit more relaxed where casual clothes will be ok at an Inn or Pub. Hotels would be smart casual.
Dinner - definitely smart clothing at a good restaurant or hotel.
2. Breakfast presumerably taken in B&B or hotel. Can be casual but feet should definitely be covered - bare feet a big no no. Clothing should not be crumpled or very creased.
Males can wear shorts when out walking or ok for casual lunch. Long trousers should be worn in the evening and especially when dining.
Accommodation providers will normally lend you an iron and ironing board on request if required.
Trust the above rule of thumbs are satisfactory for your purposes.