From the photos and size I suspected Tabanus autumnalis but as this is a very scarce species in this area, I sent the pictures to Martin Harvey, who runs the Soldierflies and Allies Recording Scheme. He is happy that it is T. autumnalis, but said that if seen again a specimen should be caught and the underside of the abdomen checked for a dark longitudinal stripe. This is diagnostic. It is only the third record for Northants.
This species is considerably bigger than the more locally common horseflies like T. bromius and Hybomitra bimaculata or the even smaller clegs and deerflies. It is generally the smaller species that are a pest to humans. The larger ones consider us too small! They generally go for cattle and deer. One good way of finding horseflies on hot days is to leave the door of your car open in a sunny area near to where there are cattle. The flies home in on infrared radiation from hot bodies and will enter the car, where you can easily (hopefully!) trap them. Alternatively, if you don't want horseflies in your car, keep the doors shut. At a field meeting of Dipterists Forum at Speyside we parked in a lay-by on the Glen Feshie road and immediately had the giant horsefly T. sudeticus investigating the front wheel arches of the car, attracted by the heat from the engine compartment. Incidently, horseflies tend to be attracted to dark objects, so wearing light coloured clothes when out in suitable habitat may reduce your chances of being bitten.