Hoes can be confusing as there are several different sorts designed for different purposes. The one on the left is a Dutch hoe, useful for weeding between rows, but can be tricky to control near plants as you push it away from you.
Burgon & Ball's Dutch hoe was a Which best buy £24.95 + £4.95 p&p.
In the middle is a large draw hoe which we think belonged to my maternal grandfather, Victor John (Jack) Brinkworth, another keen vegetable gardener. This has had several new handles over the years. Dad's tip is to put it in the water butt before use - this makes the wooden handle swell up and stops the head from falling off. This sort of hoe is easier to use close to plants because you draw it towards you (hence 'draw' hoe). It is useful for hoeing off weeds and earthing-up potatoes. Draw hoes seem less popular nowadays, but if you look at old photos of agricultural workers this is the sort they will be using, and they would be hoeing for days on end, singling and weeding.
The little hoe on the right is know in the family as a parsnip hoe: the width of the blade = the distance between the plants within the row, which makes it easier to thin out parsnips evenly. It belonged to my Great-Grandfather Palmer and was given to my gran, Lois Palmer when she was a little girl. It is at least 100 years old. Great Grampy Palmer grew enough carrots and parsnips on his allotments to pay the rent on his cottage.