This bridge was designed by William Etheridge (1707-1776), built by a Mr White of Weybridge during 1748-50, and paid for by Samuel Dicker, M.P. for Plymouth, whose house can be seen on the skyline to the left of the bridge. Having paid for the bridge, he also obtained the right to collect tolls from users of the bridge.
The Walton Bridge was much admired for its strength, contrivance and remarkable great arch, and was even described as the most beautiful wooden arch in the world. It attracted Canaletto to paint it twice, and this is a reproduction of one of those, painted in 1754, made available by courtesy of Excelsior Direct.
This picture is shown here to provide comparison with Etheridge's similar but smaller design for the bridge at Queens' College Cambridge, built 1749-50.
The Walton Bridge's main span was 130 feet, with two side arches of 44 feet. Unfortunately, it decayed and lasted only until 1783.
The following is taken from the Gentleman's Magazine of 1750:

Description of the Bridge at WALTON.
It consists of four stone peirs, between which are 3 large truss arches of beams and joists of wood, strongly bound together with mortises, iron pins, and cramps; under these 3 large arches the water constantly runs, beside which, are 5 other arches of brick work, on each side, to make the ascent and descent the more easy; but there is seldom water under any of them, except in great floods, and four of them on the Middlesex side are stopt up, being on high ground where the floods never reach.
Just above the arch (See the Plate) we have drawn a piece of the upper end of one of the two connecting lateral beams, to show the mark of the iron pin which rivets it to the upper rail, and to another similar beam, being each about 12 inches thick, so that the whole bearing is near 24 inches. These double beams have mortisses to admit the top rail, and the transverse traces, which are also pinned together at the joints. Just under this arch is shewn, more at large, the lower end of one of the lateral beams an iron plate coming about the angle, which helps to secure its conjunction with the joists, that go underneath the arch from one side to another, to support the planking, with the bed of earth and gravel for the road.
The middle arch when view'd by the river side affords an agreeable prospect of the country beautifully diversify'd with wood and water, which is seen thro' it to a considerable distance; and it would have made an excellent back landscape; in our print, but we chose, at this time, to give a simple representation of so singular a structure, by which all its parts may be much better survey'd than in a perspective. For this purpose we took several journeys to it, and had the drawing made, and afterwards corrected by the thing it self there being no other representation, that we know, of its whole extent. The design of the bridge published by Mr Wm Etheridge, the architect, and humbly presented to Wm Dicker, Esq; Pr. 5s. shews only the 3 principal arches; so that we thought proper to give the whole, that it might be seen what stress lies on the small arches, that serve for the abutments on each side. [Note: in the reproduction of the drawing above on this web page, the side arches have been omitted]. The prodigious compass of this great arch, to a person below, occasions a very common sensation of awe and surprise, as it appears like an over stretch, or an extreme; and his wonder and attention are raised, when he proceeds to take notice that all the timbers are in a falling inclination, (there not being discoverable one upright piece) and considers also the very small dimensions of the piers that support the whole.
In passingup the bridge, when you come past the brick work, the vacant interstices between the timbers yield a variety of prospects at every step, which when at the center are seen to a greater advantage. But tho' each side of the road is very well secured by the timber and rails to the height of 8 foot; yet as it affords only a parapet of wide lattice work, and the apertures even with the eye are large enough to admit the passage of any person to thro', provided he climbs, or is lifted up, and as the water is seen thro' every opening at a great depth below, those who are not used to such views cannot approach the side without some little fear.
These openings between the braces and rails might have been easily closed with boards, but they are left so to admit a free passage for the wind and air, to keep the timber more sound, and that the least decay might be at once perceived, and repaired.
We have not yet heard of any defect or objection to this bridge, that regards the workmanship or design; and we believe it will not suffer by a comparison with any of the designs which we exhibited in Nov. Mag. p. 488. in order for those who are judges of this kind of architecture to make the comparison. If there be any thing wanting, it is only a larger quantity of earth upon it; as a greater weight would not only corroborate its parts, but the earth might be disposed, to lessen the ascent and descent; for, as at Maidenhead. Kingston, Datchet, Fulham, and perhaps all other wooden bridges, so in this, if a person is standing at rest and attentive, while a horse or carriage comes hastily over the widest arch, he will perceive some motion or spring from the elasticity of the timbers; whcih cannot be in arches of stone or brick; and it might be prevented in this at Walton, by a greater pressue of earth or pavement, which would increase its solidity, the parts being so contrived, and the abutments so secured, that it is susceptible of any weight.
It is, without doubt, a noble work, and very well worth the trouble of going many miles to take a view of it, and will be so more especially in the summer, when it will be painted over, and when that part of the country is always of itself very delightful.