Two-thirds of trains were not running in some areas of France in a strike against reforms and taxis were blocking traffic around some airports.
Cab-drivers are protesting at what they regard as a lack of regulation of rival mobile service Uber.
A protest began in Madrid early on Wednesday and action was to take place in London, Milan and other cities.
The biggest taxi associations in Madrid asked their drivers to observe a 24-hour stoppage until 06:00 on Thursday morning. More than 15,000 licensed vehicles operate in Madrid, Spanish media say.
The London protest was to start in Trafalgar Square at 14:00 BST, with taxi drivers arguing that the Uber mobile app, which originated in the US, was tantamount to a taxi meter, which only black cabs are legally entitled to use in London.
Up to 12,000 drivers are expected to take part in the protest.
The Metropolitan Police said conditions had been imposed on protesters after they failed to meet with officers to discuss their plans.
In Milan, in northern Italy, a protest was taking place throughout Wednesday, although disruption was not expected to be on a similar scale as elsewhere, with boycotts expected of key sites such as railway stations and squares. Cab drivers also staged demonstrations in Rome and Naples.
Protests were taking place in several German cities, including Berlin and Hamburg.
But the worst of the disruption was in Paris, where train services were also badly affected by strike action.
Only one in three trains was running in the Paris region, although Eurostar services were unaffected.
Unions are objecting to plans to merge the rail network operator with the train company SNCF. The company said some 28% of railway staff had walked out.
Workers were also considering whether to extend the strike into Thursday. Several regions had voted to continue the stoppage, French media reported.
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