There are a lot of old pubs with this name, usually at a cross roads, so I guessed this was the reason. This is from Highways and Byways of Oxford and the Cotswolds:
“@WE may now descend to Campden either across the fields by the Fish Inn – a small isolated public built in 1771, or follow the Stow road as far as the old sign-post known as he Four Cross Hands. These ‘hands’ point to ‘Woster’, ‘Oxford’, ‘Gloster’ and ‘Warwick’ and bear the date 1669, together with the initials of the public spirited setter-up of the post, one Nathan Izod, a member of a family which has for generations owned and farmed land in the vicinity. It will be observed that the miles indicated, being computed miles, are considerably longer than our modern ones. ”
It was necessary for such signs, as with so much else at the time to be done by individuals because roads were maintained by religious houses, but when Henry VIII closed the monasteries, everything fell into neglect, so thank goodness for Izod and others for doing their part.