A list of these would be very tedious, but examples in Warwickshire would be National Express Coventry Service 25 which passes under a low bridge by Birdingbury Railway Station, and Stagecoach Service 86 with low bridges at Church Lawford and Wolston. Most of the town service routes in Rugby -1,2,4,8,8a and the 96 Northampton route are restricted to saloons due to the Rugby Station bridge. Stagecoach D1 is similarly restricted due to a low bridge in Hillmorton. Double deckers are seen on ordinary bus routes in Rugby, on other National Express (85) and Arriva service (X84) primarily for school movements, and this precludes the service practically travelling via the Rail Station for integrated transport.
At Stratford, Service 27 Stratford-Pebworth (New Road) is pretty much restricted to saloons due to a 10ton weight limit at Welford on Avon river bridge [a lightweight 'decker such as a Routemaster could be used, but this is hardly likely!].
In Nuneaton, services along Attleborough Road are worked by saloons - double deckers could be used but only through the centre of an arched bridge on a busy road, which the bus company has long judged as being too risky with oncoming vehicles and drivers forgetting.
Service 77A Leamington-Banbury passes under a low bridge by Fenny Compton station.
Diamond service 76A/B (Tamworth-Kingsbury-Wood End) is restricted to saloons due to a low bridge between Kingsbury and Hurley, and between Wood End and Piccadilly.
There are various examples of other infrequent services (or infrequent odd journeys on more substantial services) that restrict the use of double deckers.