I suppose a basic timer could do the trick. It's no longer an economy 7 tariff but would rather it only on part of the day
Ok, so excluding the earth connection, it's a simple two wires in and two wires out.
L on terminal 1, N on 2, N out on 3 and L out on 5.
Terminal 4 would be a connection to a boost immersion, or can be linked to terminal 5, to offer the boost function on a single immersion cylinder.
Your options depend on the functionality you desire and what you want to spend.
The most straightforward, but pricier option, is to replace with another Horstmann, as in the previous link - this has the benefit of a straight swap, using the original backplate, and the option to use a boost (dual) immersion (as you mentioned earlier).
Otherwise, the cheaper choice would be a standard immersion timer (as no need for economy 7) i.e.
Smart immersion timers are available from the likes of Amazon, but then it may be pot luck whether you get a decent one, with their off-brands.
Or the cheapest option, persist with investigations into your original Horstmann, take off the back cover and see what the battery looks like...