You will have no problems. I have installed an outside weatherproof socket and have the 3 Pin Ohme Smart Charger fitted to the wall and do exactly as you intend. The current draw will be 10 amps which is not excessive. The socket is on a spur from a 32A Ring and the feed to that socket is 2.5mm 3 core. The weakest part of the system is the 13 amp fuse in the plug of the Ohme charger followed by the 1.5mm 3 core flex on the Ohme charger. I too use the 4 hour Octopus Go window and manage to load about 9.5Kw to the car in that period. That's about 2.4Kw loading. To give you an idea and to allay the scare mongering that you are going to burn alive in your bed, most built in ovens are plug in 13A devices and operate for 2 to 3 hours cooking on most days with over a 2Kw load. In short, the socket in the plug will not normally be a source of any heat dissipation. Heat can only be generated where there is resistance to current flow. Normally in times gone by, that would be due to poor connections of cables in sockets or plugs, normally due to incorrect torque on the clamp screws or the wrong size of cable. Luckily all modern appliances come with preformed plugs and as long as your feed socket is on a 32A ring and in good condition you should be fine. My only concern, and it's only a mild one, would be the current rating on the timer plug and how resilient that is to 4 hours at 10 Amps. If it is from a reputable source then I think all should be fine.
My installation including the Ohme Charger was less than £250. I didn't qualify for the grant of course as it's not considered as a fixed installation but it's as good as and if you can survive on slower charge rates it certainly saves the hassle of additional work on the distribution panel, running 10m armoured cables or possible difficulties with earthing spikes etc.