Depends on how tight whether you need super cheap or big impact on a budget. Also whether you mind second hand or not.
If you don't mind second hand trawl the charity shops and boot fairs for book and games. Also ask on freecycle for board games and puzzles, sometimes you can be really lucky get someone clearing out 
. Board games are great because they are big.
I'm not great at homemade presents but I have done a DIY spy kit (rear view glasses, spy newspaper (old newspaper mounted on card with eye holes), fingerprint kit (ink pad), fake moustaches (joke shop), magnifying glass etc (Google has loads of suggestions.) And an outdoor survival kit (first aid kit, paracord bracelet, solar powered torch etc). Both ideas came off mumsnet and went down really well. The spy kit I just put in a zip file with a list of contents.
Scooters have always been a good one for us. They have the same wow appeal as a bike but at a fraction of the cost.
Same with dolls prams and pushchairs. Especially those £5 ones. Try themeing presents. So example if you got a pushchair, pick up some cheap accessories (poundland always good) like a bottle doctors kit etc. Wrap each one separately but group them together either in a gift bag or as a pretty pile of presents with string. The smaller presents will mean more because they are all connected to the larger present. Eg frozen Disney Dvd (2 for1), else doll (check out Ali express), book(charity shop), game, themed bubble bath, themed chocolate, bubbles (whatever else you can raid from poundland).
Think how you present presents in general. Wrapping presents slow kids down and is great if you have a few big boxes to bulk stuff out. Also wrap things they might not normally get food and drink wise e.g. milkshake powder, ice cream sprinkles, poundsaver disney cookies (£1 in a gorgeous tin). Consider making them take it in turns unwrapping a present at a time. Increase the ritual, take time over the thank yous etc
Keep back clothes for Christmas. Not just socks and pants but stuff like tshirts and jumpers too. Winter coats can be good if you can keep an eye out in second hand shops, boot fairs and ebay.
Hope some of the ideas might be helpful.