Bond prices are normally quoted as clean prices. The clean price of a bond is the actual price that will be paid (the dirty price) less the accrued interest. The clean price of index linked gilts also usually excludes the adjustment made for inflation to both principal and interest.
The reason markets use clean prices is that the dirty prices fluctuate with interest payments. This means that clean prices show the underlying trend in prices more clearly.
Consider a £100 bond with a 10% coupon rate and the interest payment about to be made. If the dirty price is £105 and the clean price £95, it is easier to think of this as a bond trading at £95 with £10 interest due, than as a bond worth £105, the value of which will go down to £95 once the coupon is paid.
The dirty price will fall by £10 when the interest is paid (other things being equal). This is a regular occurrence for most bonds. This means that the price of a bond will show a pattern of sudden drops, followed by gradual recoveries (a "sawtooth" pattern), that will obscure underlying trends.
The clean price will be unchanged by the interest payment, because the fall in the dirty price will be balanced by the equal fall in the accrued interest.