The round-trip cost
On a £1.2M sale plus £1.2M onward purchase: SDLT at standard rates is roughly £61,250 on the buy[HMRC SDLT], agent fees on the sell ~1.0 to 1.4% (£12k to £17k), legal both sides £4k to £7k, removals + temp accom £3k to £8k. Total friction £85k to £110k for the same square footage in the same school catchment. Buying up to a larger house adds materially more SDLT.
End-value math vs buying up
If you KDR for £450k all-in and the post-completion comparable lands £1.75M, you have added £550k of value at a £450k cost net of land. The same £550k uplift from buying up costs roughly £680k after friction. The KDR math holds in school-catchment-locked postcodes; it weakens where end-value ceiling is capped by street comparables.
Lifestyle factors
School catchment, garden orientation, commute, neighbours, established landscaping. These are the non-financial reasons most KDR owners stay. If any of them no longer fit, sell-and-move is the right call regardless of the math.