None. There is no chance of such a tunnel being built now.
The point I was making was that the opportunity to build a tunnel may have been in the past, but guess there was no goods transfer across the Humber that warranted it at the time.
While I don't see a tunnel being built currently as the current government I'd fairly anti infrastructure, particularly public transport infrastructure, I do think a tunnel would be viable. The combined population of North East Lincolnshire, North Lincolnshire, and Lincoln is around 450,000 and the population of the Hull urban area is around 500,000. That's a significant population that essentially had none existent public transport connections. A rail tunnel could quite easily achieve a 30 minute journey time between Hull and Grimsby, and a Hull to Lincoln in around an hour. That's quicker than the car journey between those places.
Cost wise I'd estimate it'd be cheaper than £500m. All of the stations already exist. The connecting lines exist on both the north and south bank, although its possible they would need to be upgraded. A tunnel was built under the humber for £100m a few years ago so it's definitely possible.
Hull and Grimsby are fairly intergrated, with Grimsby being somewhat dependent on Hull for higher education and health services. Yet the transport connections have always been awful. There used to be an express bus service between Grimsby and Hull but this gradually got intergrated with local bus services. It takes around 90 minutes today. Its also been under threat of disappearing altogether. The barton line has been awful for years with poor connections, expensive fares and terrible reliability. Its not really a surprise the humber bridge is not overly well used because of you commute from Grimsby to Hull and don't have access to your car for a day, the alternatives are non existent. That doesn't create a successful, intergrated economy.