We have almost the same situation! Small house, 2 year old and nowhere to put the mountain of large plastic things.
If she likes the park you could try a Scuttlebug. It’s like a trike thing with no pedals they just walk themselves along and steer. DS loves his and they fold down so don’t take up as much space. They are in B and M and Asda had some for about £20.
I quite like the pop up tunnels and tents (Ikea were doing them not sure if they still are). They fold down when not in use and are hours of fun.
We’ve tried to look for multifunctional toys this year.
We’re getting a Leapfrog story cube. It plays songs, reads stories and you can make your own recording of a favourite story. It also has a night light projector with a little animation. It is £35ish on Amazon if I remember.
I’ve also seen a little wooden box with a lid that has a chalkboard on one side and a magnetic whiteboard on the other. They had animal magnets with it but I saw a Peppa Pig one if your DD is a fan. The animal one was about £10.
Amazon had some projector torches in loads of different themes from animals, space to Frozen and they’re all about £6-£11.
I’m looking forward to seeing other replies for more ideas!