I haven't read all the comments so hope I'm not being repetitive.
It's hard to motivate yourself after being at work all day and all you want to do is eat, watch rubbish TV and then sleep. I found myself in this cycle and now my clothes are tight and my vanity is pushing me to address my weight gain.
But, you're not being unreasonable and your concerns are valid. Heart Disease and Diabetes are top of his "potential" life threatening issues which are also affecting a huge proportion of the UK. Prevention is very high on the agenda for the NHS and Public Health agencies.
Before you do anything you definitely need to get your husband onboard rather than by stealth. And make changes together as a family so you can support each other.
I would suggest encouraging small incremental changes try one for a few weeks, get used to it then introduce another etc e.g.
...reduce sugar in tea/coffee by one spoonful at a time. Change from full fat milk, to semi skimmed milk, to skimmed.
....change from caffeinated hot drinks to herbal drinks....
....the gym doesn't work for a lot of people, especially when they feel tired and it becomes an expensive waste. The evenings are brighter and warmer now so as a family, after eating go out for walks a few evenings per week. Slowly build up from a short walk e.g. 10mins there and back (total 20minutes). Or get a dog (if you can afford/have space/like dogs)....
Eat less red meat switch to quorn..
Reduce carbs and load up on vegetables...
The list is endless and loads of info floating around on the internet.
But..ultimately your husband must want to make the changes for himself as well.
Good luck 