Don’t understand our Oil Boiler System

We moved into our house 4 years ago, it was previously run off a back boiler system but the old owner had an oil boiler with an unvented thermal store installed to help with the sale but this was done very shortly before they moved out so I don’t know if they really understood it their self.

I have a Worcester Bosch Greenstar Danesmoor Syst Ext 12/18 ERP+ boiler outside the house against the exterior wall. Upstairs in my boiler room (directly above and next to this) I have a Gredhill Torrent thermal store installed. We have 2x thermal solar panels on the roof. Roof is a velux loft conversion so should be insulation and we have 5x radiators downstairs, 3x radiators and 1x towel rail upstairs and 2x radiators and 1x towel rail in loft. Some single and some double panel.

My Drayton lifestyle module is on a timer to come on at 4.30am until 10am and then back on at 4.30pm until 9.30pm. The problem is we just don’t ever seem to have heating or hot water available past or even sometimes during these times as it seems to have run out and my wife is sick of not getting a hot shower or bath in the morning so need to try and sort this out. Is this due to the timer? I have previously set the boiler to ‘ON’ but we just seemed to be constantly burning through oil as if the system never reached a point to cut itself off. Are they just inefficient or am I doing something wrong/missing something? Our house also never seems to get that hot although the radiators are hot to touch but this may well be a separate issue in itself - 1950s build semi detached which I’ve been told by previous owner had a council led scheme to fit cavity wall insulation although I’ve not checked this out myself yet.

A few photos attached of the setup/system just to see if anyone can help out with how I should be set up? We previously had a gas boiler in our old house so never really had any experience with this kind of set up so would appreciate any advice. Also happy to pay a tradesman to sort any issues out but just don’t know where to start or who I need exactly to do this so wanted to ask here first. Thank you!