fellow sufferer here!
badmamma,one thing to remember is that even if you've done the same local cinema, swimming, indoor playcentre thing a hundred times, and are sick to your back teeth of it,(by March each year this is how I feel), you can bet your bottom dollar your sons won't be bored. When my son (8) sees a film he likes he would happily go again the next day, and the next....
For a day trip on a rainy day, I've found the seaside is surprisingly good. Splashing about on the beach, big waves to marvel at if it's windy, followed by indoor play in arcades or play centres - pick a really commercialised seaside location - avoid unspoilt and quiet - and you can't far wrong here.
If you're in SE London, I recommend the Isle of Sheppy. About 30 mins past Bluewater.
Also - shopping - strange as it may seem. Let them loose in a big and tolerant toy shop. Ask them to think what toys they'd like for christmas, you are not there to buy big toys now. Then home to write a present list to santa.
Again if you are in London a huge thumbs up for the food halls, Egyptian hall and lifts at Harrods - great free entertainment! near enough to the natural history and science museums to combine with a visit.
Or indoor winter sports centres, with toboggan runs and real snow. Good for spectating - lots of cool snowboarders to watch, and if your sons are old enough (check the age limit beforehand) they can hire a toboggan or ice skates.
Or a large indoor boot fair. An early morning activity, so hopefully they'll be tired by the evening. If you give them a little money each, they can buy some secondhand toys to play with when they get home.
Find out what local schools are holding christmas fetes and fairs in the coming weekends. You don't have to belong to the school to go. Lots of cheap stuff, entertainment and running around possibilities virtually on your doorstep.
HTH