Apart from the fact that paying stamp duty is a hefty burdon when at the point of making a house purchase and restrict movement, the thresholds further make the calculations very unfair and distort the market.
What results is a "pooling" of properties with prices just below the threshold figures, then a significant jump to the next level of prices, eg £124,999 then a jump £150k and also £249,999 then a jump to £275k, etc.
This is unfair on people wanting to move to a property which means a jump across the bands as the difference between the two properties may be artifically stretched and then the difference in Stamp Duty is disproportionately inflated too.
This is also unfair on people selling a property which should be valued above the threshold, but is pulled down by the "pooling" effect, so they don't get the true market value for their sale.
There is no need for a set of thresholds. Using a single rate is fair and will automatically mean that the lower price sales attract less tax and the higher priced sales attract more tax, which is the reason for the thresholds in the first place.