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May confronts Labour and Lib-Dem leaders, before most of the country, about European discontinuance (12)

"May" - CAN (common substitution when asking or giving permission)
"confronts Labour and Lib-Dem leaders" - C + L + L
"most of the country" - (N)ATION
"European" - E
"discontinuance" - definition

Krautrockers sound, shift at number one, backing stoppage (12)

Krautrockers - Can
Sound shift - sell

Scrubbing the shelving(12)
Double def

Anti-establishment? (12)

The ditching of a shoddy cello, a tin can soundalike. (12)

anagram of cello a tin can
anagrind = shoddy

Ancient local engineered annulment (12)

Anagram "engineered" of "ancient local"

I see that seamus has used "annulment". I'll change mine to

Local ancient engineer retirement. (12)

Left after clean break, external body charged compensation (12)

"Left" - L, "clean break" - ANCEL, "body charged" - CATION
"compensation" - definition

Dropping Eric Cantona wasn't right but he was carrying a couple of pounds (12)

Dropping - def and anagrind

ERICCANTONA - R +LL Anag

Abandonment of taxi cut off by crowd in race (12)
Taxi cut off = ca(b)
Crowd = cell
Race = Nation