What would you prefer?
You live in a house that is adequate for your needs, could be made a bit bigger downstairs, you could lay it out in a way that suits you and increase the value by what you spend on it. The bedrooms are ok, master bedroom could do with being a bit bigger but you do have a lot of stuff. It's in a nice area, only one detached neighbour because of the small kids park on the other side of the house.
A bigger house in your budget (but still costing a lot more than the extension on your current house) but it's on a less desirable estate. The crime stats for that estate are a bit higher and it would be further to walk to the pub, the shop, river, school by about 5-10 minutes depending on how far into the estate you go. The nicer estate is on the river and it's smaller so it feels friendlier but house prices are higher.
You don't need a bigger house but it would be a nice to have. You would likely still have to make compromises and potentially have to do work on the house that you have already done to your current house.
Or you could do both but long term. Extend short term, enjoy living in the new space whilst keeping your eye out for the perfect house that ticks both location, size and budget. It could take a while but is it better than moving to somewhere that isn't as nice asap just because it's bigger.