You're struggling, the north east coast has to be the worst stretch of coastline in the UK when it comes to small boat facilities.
Humber bridge:- There's the lifeboat access on the beach at Hessle on the north end of the bridge. If you drop on when someone is at the station, they will unlock the gate for you for a donation. I wouldn't launch there, the beach is rocky & the tide is fierce, 75% chance of damage to boat.
There's a marina at Hull, afaik there are no facilities for day launching small boats.
Easington:- there used to be a guy who would tractor launch you off the beach, dunno if he's still there.
Between Spurn & Scarborough all you have are beach launches at Skipsea, Hornsea, Bridlington, Filey. These require tractors. We used to use Brid a lot, but the launch & recovery can be traumatic, you need a good bunch of strong blokes/divers in all but absolute flat calm weather.
The only launch we use now is Whitby, it costs £21 but that also includes car parking, so all in all not too bad & well worth the ease of launch/recovery. That's as long as you don't get a team of pissed up Geordies trying to launch jetskis
There were plans a few years ago to completely redevelop the harbour at Brid & build a marina, new shore line, the full works. This got objections from all the silver haired Grannies who retire to Brid to wait for the Grim Reaper, they claimed it would lower the tone of Brid, yeah right