Green’s Dictionary of Slang

trolleyed adj.

[off one’s trolley under trolley n.]

drunk or under the influence of drugs.

[Ire]Sun. Trib. (Dublin) 12 May n.p.: ‘Half a bottle of Pernod and a naggin of Paddy,’ said Fionnuala [...] ‘Good.’ Róisín said. ‘Bring them over. You can’t really do this properly unless you’re trolleyed’ [BS].
[UK]Guardian G2 5 Oct. 5: The British have that many, and more, to describe getting getting drunk. Plastered, wrecked, trolleyed [...] and arseholed are but a few.
M. Forsyth Short History of Drunkenness 4: Even those who have long stopped breathing like to get trolleyed now and then.
[Aus]G. Disher Peace 146: ‘Pissed as a fart.’ ‘Trolleyed’.