The second was a few yards west of Hungerford Bridge and was almost certainly built for the Festival of Britain as it was gone by 1954.
The link between these bridges and the counties of South-East England is a little tenuous, but as the bridges mentioned connected with the Surrey Shore of the Thames ..... !
Judging by the photograph
here, it appears that you are correct about this bridge serving the Festival of Britain site.
Having regard to the fact that the Festival of Britain site gave way to the South Bank cultural complex, one might have thought that the bridge might have remained
in situ to serve those. But maybe the fact that it was a bailey bridge meant that it could not be expected to have more than a short operational existence.