Just for fun, any ideas on potential costs? As a starting point the figures for a combined road and rail bridge were stated as being £ 4 000 000 in 1930, however the L.N.E.R. didn't consider that their share of the capital costs would ever be recouped so a proposal went before Parliament for a road only multiple span crossing at a mere £1 725 000. This gained approval but was scuppered by the Government, in a time of financial difficulty, by withdrawing its agreed contribution. Tunnels were also costed at £4 600 000 for twin bore railway tunnels of 18 feet diameter and £ 7 200 000 twin bore road tunnels each of 27 feet diameter.
Is there currently a requirement for a 'high level' bridge?
I am not sure I am aware of any large scale navigation of the Humber by large vessels at the present time.
Since the bridge would likely only be relatively lightly used a low level span with a swing/lift section should probably be considered, and if there is no need for 'high level' passage hten a solid low level bridge would probably be cheaper.
A tunnel would probably be roughly 3km long with a curve to join the railway north of the River East of Hessle where there is nothing between the line and the shore but a dual carriageway.
Using a combination cut and cover, and immersed tube tunnel would likely be the cheapest option, or by following a similar alignment with a flyover and bridge if the bridge option is selected.
As to cost, the Immersed Tunnel option for the Forth Bridge replacement was priced at ~£450m but that was for a considerably larger cross section road crossing with all the attendant additions in terms of guaranteeing air quality.
Given the generally comparable span you would probably be looking at ~£200m for such a scheme.
Which is very expensive.
Bridges are harder to price but a single track bridge is likely to be considerably cheaper.
It is worth noting that even at £200m the interest+capital repayments on such a crossing would likely only be £5.5m if it is linked to inflation. (Using the Current IL Treasury bond rate of 0.09%)
£5.5m a year sounds like a lot.
Currently six days a week there are nine trains a day arriving at Barton-upon-Humber, with four trains a day on Summer Sundays.
Assuming 'Summer' is just half the year, that implies something approaching 26 Sundays with trains, or a total of 104 trains on Sunday.
The remaining days of the week add a further ~2815 trains, giving us 2919 trains per year.
That translates as £1800 per passenger train which would presumably be extended to Hull.
Which is an awful lot if the trains are all 1 and 2 car multiple units.
But I do wonder if there is some chance for rail to grab some more market share here as the journey time from the areas along the line to Barton to Hull is probably going to competitive with alternate means of transport if the crossing were to be constructed.
Additionally, a chord constructed onto the branch from the Immingham access could potentially allow freight trains to operate over the bridge and then loop through Hull on the circle of track apparently provided in the centre and head back along the line towards York.
But I am not sure if there is any demand for such traffic.
In short, at a price of ~£200m the line would not be competitive but if a bridge (or indeed a tunnel) could be constructed for less than that then perhaps you would be in with a shot of making it competitive.
It is nowhere near as uncompetitive as I thought it was going to be when I started calculations though.
Could probably work out some reasoning behind supporting the project if you could set up a P&R scheme for hull on the south bank with a unit doing shuttles through New Barton even when trains from the south were not passing over it.
EDIT:
Apparently the ~4km immersed tube tunnels used on the Oresund Link were something like $600m, but included motorway tubes and rail tubes as well as an escape gallery which tends to imply something like $240m if an escape gallery is added to a single track railway tube.
That translates to something like ~£150m.
So maybe its no so hopeless after all.