Is there something like a "Universal 2.4GHz Receiver" for wireless peripherals?

Solution 1:

To answer the question at hand, I don't think there is something like a universal receiver for wireless peripherals.

But, you might be able to get a replacement for that part from Microsoft directly. They have an interesting knowledgebase article, How to replace Microsoft software or hardware, order service packs, and replace product manuals, which outlines the process.

You told me on chat that you're from the UK and I couldn't see any contact information for the UK in that article. So, I took the liberty to contact Microsoft and inquire about this information:

For hardware replacement, you can contact Microsoft Direct Services at 0800 032 4479¹. They are available on weekdays from 8:00 A.M. to 6:00 P.M. (excluding Bank holidays)

¹: Calls provided by BT to the 0844 number above will be charged at 5 pence per minute. A Call Set-Up Fee of up to 6 pence per call applies to calls from Residential lines. Mobile and other providers? costs may vary. See http://www.bt.com/pricing for details.

Solution 2:

The only way you'll be able to get a new receiver is by writing off to MS or whoever market the keyboards. AFAIK, the MS keyboards (And most other wireless keyboards) use their own communication schemes. You could, in theory, build your own reciever with an XBee and an Arduino, but it wouldn't be worth the work.

TL;DR: No. You can't.