Oh great, a thread in my area of expertise!
We live in an old (but beautiful) house - many windows single glazed - previously lots of draughts.
Interlining is most definitely the way to go - you can either use interlining, sandwiched between the lining and the curtain, such as this or use bonded lining, which is a fleecy interlining already bonded onto a lining, so you only need to sew one lining on, like these ones.
Instead of ordering online, you can get really good bargains if you have a curtain factory shop nearby - I generally manage to pick up interlining at about £2 a metre, so long as I am prepared to buy roll ends and join them.
If you are only going to go for a lining, black out lining is more effective at keeping out draughts than any of the so called thermal linings.
Once you decide which you want to go for, I am happy to advise on how to do it.
One of the other things I would suggest is to ensure that your windows are properly sealed - no point having double glazed windows if there are huge gaps either side of the frames.
Also doing things such as insulating the loft makes a huge difference, and if you buy those space blanket rolls from B&Q when they are on offer, it reduces the cost and hassle of laying them.
Draught proofing doors helps, as does a heavy curtain over the front door.
Searching out gaps and holes and using expandable foam (you would not believe the gaps that we have found, after a bit of detective work - again, usually around window frames and behind skirtings.
We are almost 10 years in our house now, which when we first moved in was unbelievably cold - now I would venture to say it is actually quite cosy. Am thinking of chaining my MN name to TheDraughtDetective!