Warranty Issue

C.O.Y.B.I.B

Just a scenario id appreciate some opinion on. Dont want to go into too much detail , but should be enough here for gratefully received opinions.
My bike had an issue and I dropped it back to shop where I bought it , 14 months previous. They said it wasn't a warranty issue and parts were difficult to source so might take a week or so. I thought it should be a warranty issue so I contacted the manufacturer who after a lot of to and fro with the shop (photos etc...) agreed it was under warranty and agreed to ship an original part from China with no estimated date of delivery. Its now been 5 weeks although only 1 week since the part was shipped , since I dropped my bike in and I am still bikeless and paying parking every day.
Obviously im getting frustrated , but Im not sure at who I should aim my anger. Bike shop told me if id been willing to pay for the repair it would have been done 4 weeks ago with an OEM part. If Id known it was going to take 5 weeks (and counting) obviously I would have taken this option. Putting it into the context of a car , I would be expecting a replacement car while the repair was being done especially on a warranty issue.
The bike shop will say that the delay was on the part of the manufacturer.

Bottom line is , am I right to be pssd off and who should I be pssd off at ?

Alek

http://europa.eu/legislation_summaries/consumers/protection_of_consumers/l32022_en.htm :

When a lack of conformity is notified to the seller, the consumer will be entitled to ask:

for the goods to be repaired or replaced free of charge within a reasonable period and without major inconvenience to the consumer;

Unfortunately, it seems there is no specific time frame.