Your specimen looks like Jasper, it is very common down the Yorkshire coast - especially on the Holderness.
May I suggest to you the hobby of Lapidary? polishing stones found on the beach with a stone tumbler is very interesting, i remember picking up pebbles when they were wet and putting them in my pocket only to take them out dry and looking nothing like the pebble i found.
In 1970 Herbert Scarfe brought out a book called Collecting and Polishing Stones, i am sure it is out of print but obtainable from the internet.
The author had a lot to do with our area.
I have attached a couple of images of pebbles from the Holderness that i have tumble pollished.
Have a look for the book i mentioned but in short you have a machine that has a rotating barrel on it, in the barrel are pebbles, water and abrasive powder.
You turn on the machine and leave it for sevaral days, experience will tell you when to change from a course grit to a fine grit as the pebble gets shinier and then to a final polishing medium.