Could be a good idea in time. We have a 16yo who leaves all lights on and all doors open. Smart heating would be easier, maybe next payday. Smart lighting I'm not sure, with all new smart bulbs it could take years to recoup the cost. All downstairs lights are spotlights, probably 15 in total
Smart heating controls are probably your best bet, it really depends on your boiler, but keep in mind that if you want to replace it with something truly smart you are likely to need to get a gas safe registered plumber to do the wiring for you. I use a Nest thermostat and it's great, it learns your patterns and adapts the heating schecdule to your needs, I can turn the heating on from the couch but equally if there is nobody in the house then the heating doesn't get turned on in the first place. If you have a boiler capable of opentherm then you can run the boiler at a much lower overall output and save money even more.
Replacing the existing lights with LED bulbs if not already done can result in savings - but keep in mind that smart lighting isn't neccessarily that good at reducing bills. Wifi enabled bulbs use more power in the first place and cost a bit more, but you can set up a smart home routine to turn them all off at a certain time of night which could save money. In practice I found that the savings don't really add up - it costs around £10 per bulb compared to around a quid for a regular LED light bulb and even if you left them on all day every day at 8w per bulb the total cost is only around £15 per year per bulb. It's the same with smart radiator TRVs, they don't save you any energy really - the only difference compared to a regular TRV is that they display the temperature target they are set at. And that doesn't help with spotlights, just the ones you have upstairs.
An alternative would be to try smart light switches - but that is a whole different kettle of fish as they generally require a neutral feed to the switch, which most UK houses don't have they have a live loop. You could try Quinetic - they have a wireless switch ecosystem which includes app connected toggles on some of the options, but those tend to be quite expensive and you'd have to decide for yourself whether the financial cost/benefit is worth it.
You also mentioned you have electric heating in the garden room - depending on how it's set up it might be more cost effective to swap to using oil radiators - they tend to work really well, I use one in my office and it doesn't cost much to run and saves putting the heating on for the full house.
My last thought is electric showers - they are cripplingly expensive at the moment, when we moved we took out the old electric shower and ran a feed to the hot water and installed a mixer shower - even though prices have dropped a bit it's still 5x more expensive to run an electric shower than a mixer. Most showers are around 7kw output, a quick estimate means that a family of 4 with a 15 minute shower each, once a day will spend just under £3 per day on the shower, compared to 75p for a mixer, run that difference out and you save between £400 and £600 per year.
I think you've probably realised that the most cost effective method of dealing with most of the things is to to get your kids to change their habits with lights and doors though.
