The dirty price of a bond is the actual price paid for it. It contrasts with the clean price which is adjusted for accrued interest.
Because the dirty price should be the price that is actually paid, the dirty price of an index linked gilt usually includes the effect of the inflation adjustments to the payment, rather than being quoted in real terms (based on the time of issue) as clean prices are.
Whenever a coupon payment is made, the dirty price immediately falls by the amount of the coupon. These sudden movements unrelated to valuation issues are what makes it easier for investors to think in terms of the clean price.
Obviously, even though the clean prices are what is quoted, buyers and sellers need to know the dirty prices as well