Stuff like HIIT/ circuits/interval training is fantastic, but it's much harder to motivate yourself and do it properly when you're at home rather than in a class. You also won't have equipment so are going to be limited to bodyweight stuff.
I do a lot of that sort of thing and I do get benefits from the stuff I do at home, especially since I bought a kettlebell and started regularly chucking that about, but if I'm honest I know I work harder in my weekly circuits class then when I'm in my living room.
So, first on the list - find a circuits or HIIT class near you. Problem is though, you're going to be paying £5ish a time, so - although you said no gym - I honestly would look at what your local council gym offers as it might work out less than a weekly class.
Memberships in my area are only 20 or so quid a month, so if you even only went there 3 times a week that's less than £2 a session. And of course you'd then have access to a pool and could take the children too - voila, fun family exercise, all included in your gym package!
Pilates is good for strength and core stability but won't make you lose weight or improve your cardio fitness. I do it to improve my running form, but I see it as a therapeutic thing rather than exercise IYSWIM.
DO you have a bike and access to hills? Good hilly bike rides are great exercise, not so much tootling along on the flat.
It's a shame you've ruled out running as that would be the best way to get fit and burn calories quickly. I don't think anyone "enjoys" it at first, and most people have joint issues that niggle when they start, but it quickly becomes addictive.
The key though is to find something that fits in with your lifestyle and that you can stick to. I've never known anyone stick to doing exercise DVDs for years, but cycling/running/weights - definitely. Best of luck.