Firstly I'm no heating expert, but I've been researching boilers, temps and flow rates over the last few days because of an issue with my new boiler on my thermal store. So i've accumulated alot of info on it in the last 48 hours!
Looking at your graphs (how did you measure and log this by the way?) It looks like you've got a low temp rise across the boiler feed and return and low heat transfer to the store (I take it, it's and indirect store?).
That says to me that the flow rate through the boiler is far to high? If you had a lower flow rate (slower pump) then the temp difference between the boiler return and flow would be greater, but the water would be circulating through the store coil alot slower and be able to transfer more heat to the store, and thus the water returning to the boiler would be alot cooler, the boiler would then add alot more heat and so on.
It looks like the flow rate is too high, the water is coming back to the boiler at almost the same temp it left, your boiler is seeing the high return temp and just shutting off and going into anti cycle, once it reaches its max temp.
Quite HOW you turn down the flow rate I don't know. You'll need an expert in your boiler for that!
sorry -edit to add that someone said all that a couple of days ago!
So I would find the pump, and put it on speed 1.
If there is no pump speed switch, see if there is a flow balancing valve on/near the cylinder and close it to 3/4 turn only.