If it is a British Build I don't see how it can be legal as all British held L1A1 rifles became "Section 5" after the Hungerford tragedy banning all semi auto rifles above .22.
In the UK you are not allowed to convert a "Section 5" semi auto gun to "Section 1" straight pull nor may you use any pressure bearing parts that were once on a "Section 5" rifle to create a straight pull rifle.
Section 5 is a UK classification and therefore only applies to rifles in the UK, this means parts from rifles outside the UK in theory can be used to create a straight pull but this interpretation is a very grey area.
I have two straight pull L1A1 rifles both built on Australian actions with Italian barrels which appear to be ok with the powers that be as they have passed through the proof house without any problems.