What is a reasonable timeframe for a warranty repair?

[GMac11]

I sent a Tamron lens off for repair to the lens mount. The lens arrived at the contracted repair company but has been sitting for coming up on 4 weeks. In fairness to the repair centre they had been in contact and have blamed the hold up on a lack of parts to actually do the repair.
Fortunately the lens isn’t critical with regards to paid work or anything but it did cost me £1400 and has been sitting on a repair bench for a month. I’m now starting to get to the point where I need to see some action.

As per the title, is there a reasonable amount of time that one should expect a warranty repair to be carried out? Or indeed is there even a legal timeframe?

Consequently, should I decide to escalate who do I take my concerns up with? The repair centre? The retailer? The manufacturer?

 

[GMac11]

Yeah I completely appreciate the fact that the part is not available - however there must come a point where I can’t be expected to continue waiting indefinitely because said part cannot be sourced? Perhaps I’m being unfair?
Warranty was arranged through Tamron who provided the necessary documentation then I posted directly to the repair centre. The retailer have not been involved at any stage.